vandermonde_approx_1d_test
18-Feb-2019 20:28:57

vandermonde_approx_1d_test:
  MATLAB version
  Test vandermonde_approx_1d.

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #1.
  Number of data points = 18

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    4.000000
    2:    1.000000    5.000000
    3:    2.000000    6.000000
    4:    4.000000    6.000000
    5:    5.000000    5.000000
    6:    6.000000    3.000000
    7:    7.000000    1.000000
    8:    8.000000    1.000000
    9:    9.000000    1.000000
   10:   10.000000    3.000000
   11:   11.000000    4.000000
   12:   12.000000    4.000000
   13:   13.000000    3.000000
   14:   14.000000    3.000000
   15:   15.000000    4.000000
   16:   16.000000    4.000000
   17:   17.000000    3.000000
   18:   18.000000    0.000000
  Using polynomial approximant of degree 0
{Undefined function or variable 'r8poly_value'.

Error in <a href="matlab:matlab.internal.language.introspective.errorDocCallback('vandermonde_approx_1d_test01', '/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test01.m', 53)" style="font-weight:bold">vandermonde_approx_1d_test01</a> (<a href="matlab: opentoline('/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test01.m',53,0)">line 53</a>)
  yi = r8poly_value ( m, c, ni, xi );

Error in <a href="matlab:matlab.internal.language.introspective.errorDocCallback('vandermonde_approx_1d_test', '/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test.m', 32)" style="font-weight:bold">vandermonde_approx_1d_test</a> (<a href="matlab: opentoline('/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test.m',32,0)">line 32</a>)
      vandermonde_approx_1d_test01 ( prob, m );
} 
vandermonde_approx_1d_test
18-Feb-2019 20:30:25

vandermonde_approx_1d_test:
  MATLAB version
  Test vandermonde_approx_1d.

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #1.
  Number of data points = 18

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    4.000000
    2:    1.000000    5.000000
    3:    2.000000    6.000000
    4:    4.000000    6.000000
    5:    5.000000    5.000000
    6:    6.000000    3.000000
    7:    7.000000    1.000000
    8:    8.000000    1.000000
    9:    9.000000    1.000000
   10:   10.000000    3.000000
   11:   11.000000    4.000000
   12:   12.000000    4.000000
   13:   13.000000    3.000000
   14:   14.000000    3.000000
   15:   15.000000    4.000000
   16:   16.000000    4.000000
   17:   17.000000    3.000000
   18:   18.000000    0.000000
  Using polynomial approximant of degree 0
{Error using <a href="matlab:matlab.internal.language.introspective.errorDocCallback('r8poly_value')" style="font-weight:bold">r8poly_value</a>
Too many input arguments.

Error in <a href="matlab:matlab.internal.language.introspective.errorDocCallback('vandermonde_approx_1d_test01', '/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test01.m', 53)" style="font-weight:bold">vandermonde_approx_1d_test01</a> (<a href="matlab: opentoline('/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test01.m',53,0)">line 53</a>)
  yi = r8poly_value ( m, c, ni, xi );

Error in <a href="matlab:matlab.internal.language.introspective.errorDocCallback('vandermonde_approx_1d_test', '/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test.m', 32)" style="font-weight:bold">vandermonde_approx_1d_test</a> (<a href="matlab: opentoline('/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test.m',32,0)">line 32</a>)
      vandermonde_approx_1d_test01 ( prob, m );
} 
vandermonde_approx_1d_test
18-Feb-2019 20:32:08

vandermonde_approx_1d_test:
  MATLAB version
  Test vandermonde_approx_1d.

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #1.
  Number of data points = 18

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    4.000000
    2:    1.000000    5.000000
    3:    2.000000    6.000000
    4:    4.000000    6.000000
    5:    5.000000    5.000000
    6:    6.000000    3.000000
    7:    7.000000    1.000000
    8:    8.000000    1.000000
    9:    9.000000    1.000000
   10:   10.000000    3.000000
   11:   11.000000    4.000000
   12:   12.000000    4.000000
   13:   13.000000    3.000000
   14:   14.000000    3.000000
   15:   15.000000    4.000000
   16:   16.000000    4.000000
   17:   17.000000    3.000000
   18:   18.000000    0.000000
  Using polynomial approximant of degree 0

  L2 data approximation error = 0.392837

  Normalized length of piecewise linear interpolant = 3.13553
  Normalized length of polynomial approximant       = 1
  Created plot file "p01_poly00.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #1.
  Number of data points = 18

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    4.000000
    2:    1.000000    5.000000
    3:    2.000000    6.000000
    4:    4.000000    6.000000
    5:    5.000000    5.000000
    6:    6.000000    3.000000
    7:    7.000000    1.000000
    8:    8.000000    1.000000
    9:    9.000000    1.000000
   10:   10.000000    3.000000
   11:   11.000000    4.000000
   12:   12.000000    4.000000
   13:   13.000000    3.000000
   14:   14.000000    3.000000
   15:   15.000000    4.000000
   16:   16.000000    4.000000
   17:   17.000000    3.000000
   18:   18.000000    0.000000
  Using polynomial approximant of degree 1

  L2 data approximation error = 0.350074

  Normalized length of piecewise linear interpolant = 3.13553
  Normalized length of polynomial approximant       = 1.08357

  Created plot file "p01_data.png".
  Created plot file "p01_poly01.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #1.
  Number of data points = 18

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    4.000000
    2:    1.000000    5.000000
    3:    2.000000    6.000000
    4:    4.000000    6.000000
    5:    5.000000    5.000000
    6:    6.000000    3.000000
    7:    7.000000    1.000000
    8:    8.000000    1.000000
    9:    9.000000    1.000000
   10:   10.000000    3.000000
   11:   11.000000    4.000000
   12:   12.000000    4.000000
   13:   13.000000    3.000000
   14:   14.000000    3.000000
   15:   15.000000    4.000000
   16:   16.000000    4.000000
   17:   17.000000    3.000000
   18:   18.000000    0.000000
  Using polynomial approximant of degree 2

  L2 data approximation error = 0.344057

  Normalized length of piecewise linear interpolant = 3.13553
  Normalized length of polynomial approximant       = 1.12211
  Created plot file "p01_poly02.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #1.
  Number of data points = 18

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    4.000000
    2:    1.000000    5.000000
    3:    2.000000    6.000000
    4:    4.000000    6.000000
    5:    5.000000    5.000000
    6:    6.000000    3.000000
    7:    7.000000    1.000000
    8:    8.000000    1.000000
    9:    9.000000    1.000000
   10:   10.000000    3.000000
   11:   11.000000    4.000000
   12:   12.000000    4.000000
   13:   13.000000    3.000000
   14:   14.000000    3.000000
   15:   15.000000    4.000000
   16:   16.000000    4.000000
   17:   17.000000    3.000000
   18:   18.000000    0.000000
  Using polynomial approximant of degree 3

  L2 data approximation error = 0.332868

  Normalized length of piecewise linear interpolant = 3.13553
  Normalized length of polynomial approximant       = 1.31026
  Created plot file "p01_poly03.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #1.
  Number of data points = 18

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    4.000000
    2:    1.000000    5.000000
    3:    2.000000    6.000000
    4:    4.000000    6.000000
    5:    5.000000    5.000000
    6:    6.000000    3.000000
    7:    7.000000    1.000000
    8:    8.000000    1.000000
    9:    9.000000    1.000000
   10:   10.000000    3.000000
   11:   11.000000    4.000000
   12:   12.000000    4.000000
   13:   13.000000    3.000000
   14:   14.000000    3.000000
   15:   15.000000    4.000000
   16:   16.000000    4.000000
   17:   17.000000    3.000000
   18:   18.000000    0.000000
  Using polynomial approximant of degree 4

  L2 data approximation error = 0.199123

  Normalized length of piecewise linear interpolant = 3.13553
  Normalized length of polynomial approximant       = 2.51647
  Created plot file "p01_poly04.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #1.
  Number of data points = 18

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    4.000000
    2:    1.000000    5.000000
    3:    2.000000    6.000000
    4:    4.000000    6.000000
    5:    5.000000    5.000000
    6:    6.000000    3.000000
    7:    7.000000    1.000000
    8:    8.000000    1.000000
    9:    9.000000    1.000000
   10:   10.000000    3.000000
   11:   11.000000    4.000000
   12:   12.000000    4.000000
   13:   13.000000    3.000000
   14:   14.000000    3.000000
   15:   15.000000    4.000000
   16:   16.000000    4.000000
   17:   17.000000    3.000000
   18:   18.000000    0.000000
  Using polynomial approximant of degree 5

  L2 data approximation error = 0.190907

  Normalized length of piecewise linear interpolant = 3.13553
  Normalized length of polynomial approximant       = 2.60932
  Created plot file "p01_poly05.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #1.
  Number of data points = 18

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    4.000000
    2:    1.000000    5.000000
    3:    2.000000    6.000000
    4:    4.000000    6.000000
    5:    5.000000    5.000000
    6:    6.000000    3.000000
    7:    7.000000    1.000000
    8:    8.000000    1.000000
    9:    9.000000    1.000000
   10:   10.000000    3.000000
   11:   11.000000    4.000000
   12:   12.000000    4.000000
   13:   13.000000    3.000000
   14:   14.000000    3.000000
   15:   15.000000    4.000000
   16:   16.000000    4.000000
   17:   17.000000    3.000000
   18:   18.000000    0.000000
  Using polynomial approximant of degree 9

  L2 data approximation error = 0.0613776

  Normalized length of piecewise linear interpolant = 3.13553
  Normalized length of polynomial approximant       = 3.22044
  Created plot file "p01_poly09.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #1.
  Number of data points = 18

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    4.000000
    2:    1.000000    5.000000
    3:    2.000000    6.000000
    4:    4.000000    6.000000
    5:    5.000000    5.000000
    6:    6.000000    3.000000
    7:    7.000000    1.000000
    8:    8.000000    1.000000
    9:    9.000000    1.000000
   10:   10.000000    3.000000
   11:   11.000000    4.000000
   12:   12.000000    4.000000
   13:   13.000000    3.000000
   14:   14.000000    3.000000
   15:   15.000000    4.000000
   16:   16.000000    4.000000
   17:   17.000000    3.000000
   18:   18.000000    0.000000
  Using polynomial approximant of degree 12
[Warning: Rank deficient, rank = 8, tol =  5.328830e+00.] 
[> In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('vandermonde_approx_1d_test01', '/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test01.m', 47)" style="font-weight:bold">vandermonde_approx_1d_test01</a> (<a href="matlab: opentoline('/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test01.m',47,0)">line 47</a>)
  In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('vandermonde_approx_1d_test', '/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test.m', 32)" style="font-weight:bold">vandermonde_approx_1d_test</a> (<a href="matlab: opentoline('/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test.m',32,0)">line 32</a>)
] 

  L2 data approximation error = 0.465929

  Normalized length of piecewise linear interpolant = 3.13553
  Normalized length of polynomial approximant       = 4.39868
  Created plot file "p01_poly12.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #2.
  Number of data points = 18

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    1.340000    5.000000
    3:    5.000000    8.660000
    4:   10.000000   10.000000
    5:   10.600000   10.400000
    6:   10.700000   12.000000
    7:   10.705000   28.600000
    8:   10.800000   30.200000
    9:   11.400000   30.600000
   10:   19.600000   30.600000
   11:   20.200000   30.200000
   12:   20.295000   28.600000
   13:   20.300000   12.000000
   14:   20.400000   10.400000
   15:   21.000000   10.000000
   16:   26.000000    8.660000
   17:   29.660000    5.000000
   18:   31.000000    0.000000
  Using polynomial approximant of degree 0

  L2 data approximation error = 2.58162

  Normalized length of piecewise linear interpolant = 2.66086
  Normalized length of polynomial approximant       = 1
  Created plot file "p02_poly00.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #2.
  Number of data points = 18

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    1.340000    5.000000
    3:    5.000000    8.660000
    4:   10.000000   10.000000
    5:   10.600000   10.400000
    6:   10.700000   12.000000
    7:   10.705000   28.600000
    8:   10.800000   30.200000
    9:   11.400000   30.600000
   10:   19.600000   30.600000
   11:   20.200000   30.200000
   12:   20.295000   28.600000
   13:   20.300000   12.000000
   14:   20.400000   10.400000
   15:   21.000000   10.000000
   16:   26.000000    8.660000
   17:   29.660000    5.000000
   18:   31.000000    0.000000
  Using polynomial approximant of degree 1

  L2 data approximation error = 2.58162

  Normalized length of piecewise linear interpolant = 2.66086
  Normalized length of polynomial approximant       = 1

  Created plot file "p02_data.png".
  Created plot file "p02_poly01.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #2.
  Number of data points = 18

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    1.340000    5.000000
    3:    5.000000    8.660000
    4:   10.000000   10.000000
    5:   10.600000   10.400000
    6:   10.700000   12.000000
    7:   10.705000   28.600000
    8:   10.800000   30.200000
    9:   11.400000   30.600000
   10:   19.600000   30.600000
   11:   20.200000   30.200000
   12:   20.295000   28.600000
   13:   20.300000   12.000000
   14:   20.400000   10.400000
   15:   21.000000   10.000000
   16:   26.000000    8.660000
   17:   29.660000    5.000000
   18:   31.000000    0.000000
  Using polynomial approximant of degree 2

  L2 data approximation error = 1.80946

  Normalized length of piecewise linear interpolant = 2.66086
  Normalized length of polynomial approximant       = 1.88131
  Created plot file "p02_poly02.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #2.
  Number of data points = 18

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    1.340000    5.000000
    3:    5.000000    8.660000
    4:   10.000000   10.000000
    5:   10.600000   10.400000
    6:   10.700000   12.000000
    7:   10.705000   28.600000
    8:   10.800000   30.200000
    9:   11.400000   30.600000
   10:   19.600000   30.600000
   11:   20.200000   30.200000
   12:   20.295000   28.600000
   13:   20.300000   12.000000
   14:   20.400000   10.400000
   15:   21.000000   10.000000
   16:   26.000000    8.660000
   17:   29.660000    5.000000
   18:   31.000000    0.000000
  Using polynomial approximant of degree 3

  L2 data approximation error = 1.80946

  Normalized length of piecewise linear interpolant = 2.66086
  Normalized length of polynomial approximant       = 1.88131
  Created plot file "p02_poly03.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #2.
  Number of data points = 18

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    1.340000    5.000000
    3:    5.000000    8.660000
    4:   10.000000   10.000000
    5:   10.600000   10.400000
    6:   10.700000   12.000000
    7:   10.705000   28.600000
    8:   10.800000   30.200000
    9:   11.400000   30.600000
   10:   19.600000   30.600000
   11:   20.200000   30.200000
   12:   20.295000   28.600000
   13:   20.300000   12.000000
   14:   20.400000   10.400000
   15:   21.000000   10.000000
   16:   26.000000    8.660000
   17:   29.660000    5.000000
   18:   31.000000    0.000000
  Using polynomial approximant of degree 4

  L2 data approximation error = 1.76341

  Normalized length of piecewise linear interpolant = 2.66086
  Normalized length of polynomial approximant       = 1.90124
  Created plot file "p02_poly04.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #2.
  Number of data points = 18

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    1.340000    5.000000
    3:    5.000000    8.660000
    4:   10.000000   10.000000
    5:   10.600000   10.400000
    6:   10.700000   12.000000
    7:   10.705000   28.600000
    8:   10.800000   30.200000
    9:   11.400000   30.600000
   10:   19.600000   30.600000
   11:   20.200000   30.200000
   12:   20.295000   28.600000
   13:   20.300000   12.000000
   14:   20.400000   10.400000
   15:   21.000000   10.000000
   16:   26.000000    8.660000
   17:   29.660000    5.000000
   18:   31.000000    0.000000
  Using polynomial approximant of degree 5

  L2 data approximation error = 1.76341

  Normalized length of piecewise linear interpolant = 2.66086
  Normalized length of polynomial approximant       = 1.90124
  Created plot file "p02_poly05.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #2.
  Number of data points = 18

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    1.340000    5.000000
    3:    5.000000    8.660000
    4:   10.000000   10.000000
    5:   10.600000   10.400000
    6:   10.700000   12.000000
    7:   10.705000   28.600000
    8:   10.800000   30.200000
    9:   11.400000   30.600000
   10:   19.600000   30.600000
   11:   20.200000   30.200000
   12:   20.295000   28.600000
   13:   20.300000   12.000000
   14:   20.400000   10.400000
   15:   21.000000   10.000000
   16:   26.000000    8.660000
   17:   29.660000    5.000000
   18:   31.000000    0.000000
  Using polynomial approximant of degree 9

  L2 data approximation error = 1.30404

  Normalized length of piecewise linear interpolant = 2.66086
  Normalized length of polynomial approximant       = 8.90486
  Created plot file "p02_poly09.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #2.
  Number of data points = 18

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    1.340000    5.000000
    3:    5.000000    8.660000
    4:   10.000000   10.000000
    5:   10.600000   10.400000
    6:   10.700000   12.000000
    7:   10.705000   28.600000
    8:   10.800000   30.200000
    9:   11.400000   30.600000
   10:   19.600000   30.600000
   11:   20.200000   30.200000
   12:   20.295000   28.600000
   13:   20.300000   12.000000
   14:   20.400000   10.400000
   15:   21.000000   10.000000
   16:   26.000000    8.660000
   17:   29.660000    5.000000
   18:   31.000000    0.000000
  Using polynomial approximant of degree 12
[Warning: Rank deficient, rank = 7, tol =  3.672964e+03.] 
[> In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('vandermonde_approx_1d_test01', '/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test01.m', 47)" style="font-weight:bold">vandermonde_approx_1d_test01</a> (<a href="matlab: opentoline('/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test01.m',47,0)">line 47</a>)
  In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('vandermonde_approx_1d_test', '/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test.m', 32)" style="font-weight:bold">vandermonde_approx_1d_test</a> (<a href="matlab: opentoline('/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test.m',32,0)">line 32</a>)
] 

  L2 data approximation error = 1.45992

  Normalized length of piecewise linear interpolant = 2.66086
  Normalized length of polynomial approximant       = 7.11494
  Created plot file "p02_poly12.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #3.
  Number of data points = 11

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    2.000000   10.000000
    3:    3.000000   10.000000
    4:    5.000000   10.000000
    5:    6.000000   10.000000
    6:    8.000000   10.000000
    7:    9.000000   10.500000
    8:   11.000000   15.000000
    9:   12.000000   50.000000
   10:   14.000000   60.000000
   11:   15.000000   85.000000
  Using polynomial approximant of degree 0

  L2 data approximation error = 7.87737

  Normalized length of piecewise linear interpolant = 1.68472
  Normalized length of polynomial approximant       = 1
  Created plot file "p03_poly00.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #3.
  Number of data points = 11

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    2.000000   10.000000
    3:    3.000000   10.000000
    4:    5.000000   10.000000
    5:    6.000000   10.000000
    6:    8.000000   10.000000
    7:    9.000000   10.500000
    8:   11.000000   15.000000
    9:   12.000000   50.000000
   10:   14.000000   60.000000
   11:   15.000000   85.000000
  Using polynomial approximant of degree 1

  L2 data approximation error = 4.4679

  Normalized length of piecewise linear interpolant = 1.68472
  Normalized length of polynomial approximant       = 1.28026

  Created plot file "p03_data.png".
  Created plot file "p03_poly01.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #3.
  Number of data points = 11

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    2.000000   10.000000
    3:    3.000000   10.000000
    4:    5.000000   10.000000
    5:    6.000000   10.000000
    6:    8.000000   10.000000
    7:    9.000000   10.500000
    8:   11.000000   15.000000
    9:   12.000000   50.000000
   10:   14.000000   60.000000
   11:   15.000000   85.000000
  Using polynomial approximant of degree 2

  L2 data approximation error = 2.59431

  Normalized length of piecewise linear interpolant = 1.68472
  Normalized length of polynomial approximant       = 1.48631
  Created plot file "p03_poly02.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #3.
  Number of data points = 11

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    2.000000   10.000000
    3:    3.000000   10.000000
    4:    5.000000   10.000000
    5:    6.000000   10.000000
    6:    8.000000   10.000000
    7:    9.000000   10.500000
    8:   11.000000   15.000000
    9:   12.000000   50.000000
   10:   14.000000   60.000000
   11:   15.000000   85.000000
  Using polynomial approximant of degree 3

  L2 data approximation error = 1.74627

  Normalized length of piecewise linear interpolant = 1.68472
  Normalized length of polynomial approximant       = 1.58943
  Created plot file "p03_poly03.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #3.
  Number of data points = 11

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    2.000000   10.000000
    3:    3.000000   10.000000
    4:    5.000000   10.000000
    5:    6.000000   10.000000
    6:    8.000000   10.000000
    7:    9.000000   10.500000
    8:   11.000000   15.000000
    9:   12.000000   50.000000
   10:   14.000000   60.000000
   11:   15.000000   85.000000
  Using polynomial approximant of degree 4

  L2 data approximation error = 1.68297

  Normalized length of piecewise linear interpolant = 1.68472
  Normalized length of polynomial approximant       = 1.61226
  Created plot file "p03_poly04.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #3.
  Number of data points = 11

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    2.000000   10.000000
    3:    3.000000   10.000000
    4:    5.000000   10.000000
    5:    6.000000   10.000000
    6:    8.000000   10.000000
    7:    9.000000   10.500000
    8:   11.000000   15.000000
    9:   12.000000   50.000000
   10:   14.000000   60.000000
   11:   15.000000   85.000000
  Using polynomial approximant of degree 5

  L2 data approximation error = 1.66663

  Normalized length of piecewise linear interpolant = 1.68472
  Normalized length of polynomial approximant       = 1.59507
  Created plot file "p03_poly05.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #3.
  Number of data points = 11

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    2.000000   10.000000
    3:    3.000000   10.000000
    4:    5.000000   10.000000
    5:    6.000000   10.000000
    6:    8.000000   10.000000
    7:    9.000000   10.500000
    8:   11.000000   15.000000
    9:   12.000000   50.000000
   10:   14.000000   60.000000
   11:   15.000000   85.000000
  Using polynomial approximant of degree 9

  L2 data approximation error = 0.328589

  Normalized length of piecewise linear interpolant = 1.68472
  Normalized length of polynomial approximant       = 3.28924
  Created plot file "p03_poly09.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #3.
  Number of data points = 11

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    2.000000   10.000000
    3:    3.000000   10.000000
    4:    5.000000   10.000000
    5:    6.000000   10.000000
    6:    8.000000   10.000000
    7:    9.000000   10.500000
    8:   11.000000   15.000000
    9:   12.000000   50.000000
   10:   14.000000   60.000000
   11:   15.000000   85.000000
  Using polynomial approximant of degree 12
[Warning: Rank deficient, rank = 10, tol =  4.096274e-01.] 
[> In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('vandermonde_approx_1d_test01', '/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test01.m', 47)" style="font-weight:bold">vandermonde_approx_1d_test01</a> (<a href="matlab: opentoline('/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test01.m',47,0)">line 47</a>)
  In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('vandermonde_approx_1d_test', '/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test.m', 32)" style="font-weight:bold">vandermonde_approx_1d_test</a> (<a href="matlab: opentoline('/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test.m',32,0)">line 32</a>)
] 

  L2 data approximation error = 0.205051

  Normalized length of piecewise linear interpolant = 1.68472
  Normalized length of polynomial approximant       = 4.92239
  Created plot file "p03_poly12.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #4.
  Number of data points = 8

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    0.050000    0.700000
    3:    0.100000    1.000000
    4:    0.200000    1.000000
    5:    0.800000    0.300000
    6:    0.850000    0.050000
    7:    0.900000    0.100000
    8:    1.000000    1.000000
  Using polynomial approximant of degree 0

  L2 data approximation error = 0.149984

  Normalized length of piecewise linear interpolant = 3.25908
  Normalized length of polynomial approximant       = 1
  Created plot file "p04_poly00.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #4.
  Number of data points = 8

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    0.050000    0.700000
    3:    0.100000    1.000000
    4:    0.200000    1.000000
    5:    0.800000    0.300000
    6:    0.850000    0.050000
    7:    0.900000    0.100000
    8:    1.000000    1.000000
  Using polynomial approximant of degree 1

  L2 data approximation error = 0.146011

  Normalized length of piecewise linear interpolant = 3.25908
  Normalized length of polynomial approximant       = 1.02803

  Created plot file "p04_data.png".
  Created plot file "p04_poly01.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #4.
  Number of data points = 8

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    0.050000    0.700000
    3:    0.100000    1.000000
    4:    0.200000    1.000000
    5:    0.800000    0.300000
    6:    0.850000    0.050000
    7:    0.900000    0.100000
    8:    1.000000    1.000000
  Using polynomial approximant of degree 2

  L2 data approximation error = 0.14598

  Normalized length of piecewise linear interpolant = 3.25908
  Normalized length of polynomial approximant       = 1.03194
  Created plot file "p04_poly02.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #4.
  Number of data points = 8

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    0.050000    0.700000
    3:    0.100000    1.000000
    4:    0.200000    1.000000
    5:    0.800000    0.300000
    6:    0.850000    0.050000
    7:    0.900000    0.100000
    8:    1.000000    1.000000
  Using polynomial approximant of degree 3

  L2 data approximation error = 0.0559589

  Normalized length of piecewise linear interpolant = 3.25908
  Normalized length of polynomial approximant       = 3.3304
  Created plot file "p04_poly03.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #4.
  Number of data points = 8

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    0.050000    0.700000
    3:    0.100000    1.000000
    4:    0.200000    1.000000
    5:    0.800000    0.300000
    6:    0.850000    0.050000
    7:    0.900000    0.100000
    8:    1.000000    1.000000
  Using polynomial approximant of degree 4

  L2 data approximation error = 0.0559577

  Normalized length of piecewise linear interpolant = 3.25908
  Normalized length of polynomial approximant       = 3.32957
  Created plot file "p04_poly04.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #4.
  Number of data points = 8

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    0.050000    0.700000
    3:    0.100000    1.000000
    4:    0.200000    1.000000
    5:    0.800000    0.300000
    6:    0.850000    0.050000
    7:    0.900000    0.100000
    8:    1.000000    1.000000
  Using polynomial approximant of degree 5

  L2 data approximation error = 0.00829484

  Normalized length of piecewise linear interpolant = 3.25908
  Normalized length of polynomial approximant       = 3.58478
  Created plot file "p04_poly05.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #4.
  Number of data points = 8

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    0.050000    0.700000
    3:    0.100000    1.000000
    4:    0.200000    1.000000
    5:    0.800000    0.300000
    6:    0.850000    0.050000
    7:    0.900000    0.100000
    8:    1.000000    1.000000
  Using polynomial approximant of degree 9

  L2 data approximation error = 9.36892e-15

  Normalized length of piecewise linear interpolant = 3.25908
  Normalized length of polynomial approximant       = 4.81669
  Created plot file "p04_poly09.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #4.
  Number of data points = 8

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    0.050000    0.700000
    3:    0.100000    1.000000
    4:    0.200000    1.000000
    5:    0.800000    0.300000
    6:    0.850000    0.050000
    7:    0.900000    0.100000
    8:    1.000000    1.000000
  Using polynomial approximant of degree 12

  L2 data approximation error = 2.24558e-14

  Normalized length of piecewise linear interpolant = 3.25908
  Normalized length of polynomial approximant       = 4.89584
  Created plot file "p04_poly12.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #5.
  Number of data points = 9

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    0.100000    0.900000
    3:    0.200000    0.950000
    4:    0.300000    0.900000
    5:    0.400000    0.100000
    6:    0.500000    0.050000
    7:    0.600000    0.050000
    8:    0.800000    0.200000
    9:    1.000000    1.000000
  Using polynomial approximant of degree 0

  L2 data approximation error = 0.143324

  Normalized length of piecewise linear interpolant = 3.2218
  Normalized length of polynomial approximant       = 1
  Created plot file "p05_poly00.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #5.
  Number of data points = 9

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    0.100000    0.900000
    3:    0.200000    0.950000
    4:    0.300000    0.900000
    5:    0.400000    0.100000
    6:    0.500000    0.050000
    7:    0.600000    0.050000
    8:    0.800000    0.200000
    9:    1.000000    1.000000
  Using polynomial approximant of degree 1

  L2 data approximation error = 0.143322

  Normalized length of piecewise linear interpolant = 3.2218
  Normalized length of polynomial approximant       = 1.00003

  Created plot file "p05_data.png".
  Created plot file "p05_poly01.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #5.
  Number of data points = 9

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    0.100000    0.900000
    3:    0.200000    0.950000
    4:    0.300000    0.900000
    5:    0.400000    0.100000
    6:    0.500000    0.050000
    7:    0.600000    0.050000
    8:    0.800000    0.200000
    9:    1.000000    1.000000
  Using polynomial approximant of degree 2

  L2 data approximation error = 0.13517

  Normalized length of piecewise linear interpolant = 3.2218
  Normalized length of polynomial approximant       = 1.31038
  Created plot file "p05_poly02.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #5.
  Number of data points = 9

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    0.100000    0.900000
    3:    0.200000    0.950000
    4:    0.300000    0.900000
    5:    0.400000    0.100000
    6:    0.500000    0.050000
    7:    0.600000    0.050000
    8:    0.800000    0.200000
    9:    1.000000    1.000000
  Using polynomial approximant of degree 3

  L2 data approximation error = 0.0717904

  Normalized length of piecewise linear interpolant = 3.2218
  Normalized length of polynomial approximant       = 3.05546
  Created plot file "p05_poly03.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #5.
  Number of data points = 9

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    0.100000    0.900000
    3:    0.200000    0.950000
    4:    0.300000    0.900000
    5:    0.400000    0.100000
    6:    0.500000    0.050000
    7:    0.600000    0.050000
    8:    0.800000    0.200000
    9:    1.000000    1.000000
  Using polynomial approximant of degree 4

  L2 data approximation error = 0.0391096

  Normalized length of piecewise linear interpolant = 3.2218
  Normalized length of polynomial approximant       = 3.42544
  Created plot file "p05_poly04.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #5.
  Number of data points = 9

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    0.100000    0.900000
    3:    0.200000    0.950000
    4:    0.300000    0.900000
    5:    0.400000    0.100000
    6:    0.500000    0.050000
    7:    0.600000    0.050000
    8:    0.800000    0.200000
    9:    1.000000    1.000000
  Using polynomial approximant of degree 5

  L2 data approximation error = 0.03589

  Normalized length of piecewise linear interpolant = 3.2218
  Normalized length of polynomial approximant       = 3.41454
  Created plot file "p05_poly05.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #5.
  Number of data points = 9

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    0.100000    0.900000
    3:    0.200000    0.950000
    4:    0.300000    0.900000
    5:    0.400000    0.100000
    6:    0.500000    0.050000
    7:    0.600000    0.050000
    8:    0.800000    0.200000
    9:    1.000000    1.000000
  Using polynomial approximant of degree 9

  L2 data approximation error = 3.02496e-12

  Normalized length of piecewise linear interpolant = 3.2218
  Normalized length of polynomial approximant       = 47.9536
  Created plot file "p05_poly09.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #5.
  Number of data points = 9

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    0.100000    0.900000
    3:    0.200000    0.950000
    4:    0.300000    0.900000
    5:    0.400000    0.100000
    6:    0.500000    0.050000
    7:    0.600000    0.050000
    8:    0.800000    0.200000
    9:    1.000000    1.000000
  Using polynomial approximant of degree 12

  L2 data approximation error = 9.77135e-13

  Normalized length of piecewise linear interpolant = 3.2218
  Normalized length of polynomial approximant       = 125.388
  Created plot file "p05_poly12.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #6.
  Number of data points = 49

  Data array:

  Row:       1             2       
  Col
    1:  595.000000    0.644000
    2:  605.000000    0.622000
    3:  615.000000    0.638000
    4:  625.000000    0.649000
    5:  635.000000    0.652000
    6:  645.000000    0.639000
    7:  655.000000    0.646000
    8:  665.000000    0.657000
    9:  675.000000    0.652000
   10:  685.000000    0.655000
   11:  695.000000    0.644000
   12:  705.000000    0.663000
   13:  715.000000    0.663000
   14:  725.000000    0.668000
   15:  735.000000    0.676000
   16:  745.000000    0.676000
   17:  755.000000    0.686000
   18:  765.000000    0.679000
   19:  775.000000    0.678000
   20:  785.000000    0.683000
   21:  795.000000    0.694000
   22:  805.000000    0.699000
   23:  815.000000    0.710000
   24:  825.000000    0.730000
   25:  835.000000    0.763000
   26:  845.000000    0.812000
   27:  855.000000    0.907000
   28:  865.000000    1.044000
   29:  875.000000    1.336000
   30:  885.000000    1.881000
   31:  895.000000    2.169000
   32:  905.000000    2.075000
   33:  915.000000    1.598000
   34:  925.000000    1.211000
   35:  935.000000    0.916000
   36:  945.000000    0.746000
   37:  955.000000    0.672000
   38:  965.000000    0.627000
   39:  975.000000    0.615000
   40:  985.000000    0.607000
   41:  995.000000    0.606000
   42: 1005.000000    0.609000
   43: 1015.000000    0.603000
   44: 1025.000000    0.601000
   45: 1035.000000    0.603000
   46: 1045.000000    0.601000
   47: 1055.000000    0.611000
   48: 1065.000000    0.601000
   49: 1075.000000    0.608000
  Using polynomial approximant of degree 0

  L2 data approximation error = 0.0530251

  Normalized length of piecewise linear interpolant = 2.68209
  Normalized length of polynomial approximant       = 1
  Created plot file "p06_poly00.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #6.
  Number of data points = 49

  Data array:

  Row:       1             2       
  Col
    1:  595.000000    0.644000
    2:  605.000000    0.622000
    3:  615.000000    0.638000
    4:  625.000000    0.649000
    5:  635.000000    0.652000
    6:  645.000000    0.639000
    7:  655.000000    0.646000
    8:  665.000000    0.657000
    9:  675.000000    0.652000
   10:  685.000000    0.655000
   11:  695.000000    0.644000
   12:  705.000000    0.663000
   13:  715.000000    0.663000
   14:  725.000000    0.668000
   15:  735.000000    0.676000
   16:  745.000000    0.676000
   17:  755.000000    0.686000
   18:  765.000000    0.679000
   19:  775.000000    0.678000
   20:  785.000000    0.683000
   21:  795.000000    0.694000
   22:  805.000000    0.699000
   23:  815.000000    0.710000
   24:  825.000000    0.730000
   25:  835.000000    0.763000
   26:  845.000000    0.812000
   27:  855.000000    0.907000
   28:  865.000000    1.044000
   29:  875.000000    1.336000
   30:  885.000000    1.881000
   31:  895.000000    2.169000
   32:  905.000000    2.075000
   33:  915.000000    1.598000
   34:  925.000000    1.211000
   35:  935.000000    0.916000
   36:  945.000000    0.746000
   37:  955.000000    0.672000
   38:  965.000000    0.627000
   39:  975.000000    0.615000
   40:  985.000000    0.607000
   41:  995.000000    0.606000
   42: 1005.000000    0.609000
   43: 1015.000000    0.603000
   44: 1025.000000    0.601000
   45: 1035.000000    0.603000
   46: 1045.000000    0.601000
   47: 1055.000000    0.611000
   48: 1065.000000    0.601000
   49: 1075.000000    0.608000
  Using polynomial approximant of degree 1

  L2 data approximation error = 0.0525121

  Normalized length of piecewise linear interpolant = 2.68209
  Normalized length of polynomial approximant       = 1.0062

  Created plot file "p06_data.png".
  Created plot file "p06_poly01.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #6.
  Number of data points = 49

  Data array:

  Row:       1             2       
  Col
    1:  595.000000    0.644000
    2:  605.000000    0.622000
    3:  615.000000    0.638000
    4:  625.000000    0.649000
    5:  635.000000    0.652000
    6:  645.000000    0.639000
    7:  655.000000    0.646000
    8:  665.000000    0.657000
    9:  675.000000    0.652000
   10:  685.000000    0.655000
   11:  695.000000    0.644000
   12:  705.000000    0.663000
   13:  715.000000    0.663000
   14:  725.000000    0.668000
   15:  735.000000    0.676000
   16:  745.000000    0.676000
   17:  755.000000    0.686000
   18:  765.000000    0.679000
   19:  775.000000    0.678000
   20:  785.000000    0.683000
   21:  795.000000    0.694000
   22:  805.000000    0.699000
   23:  815.000000    0.710000
   24:  825.000000    0.730000
   25:  835.000000    0.763000
   26:  845.000000    0.812000
   27:  855.000000    0.907000
   28:  865.000000    1.044000
   29:  875.000000    1.336000
   30:  885.000000    1.881000
   31:  895.000000    2.169000
   32:  905.000000    2.075000
   33:  915.000000    1.598000
   34:  925.000000    1.211000
   35:  935.000000    0.916000
   36:  945.000000    0.746000
   37:  955.000000    0.672000
   38:  965.000000    0.627000
   39:  975.000000    0.615000
   40:  985.000000    0.607000
   41:  995.000000    0.606000
   42: 1005.000000    0.609000
   43: 1015.000000    0.603000
   44: 1025.000000    0.601000
   45: 1035.000000    0.603000
   46: 1045.000000    0.601000
   47: 1055.000000    0.611000
   48: 1065.000000    0.601000
   49: 1075.000000    0.608000
  Using polynomial approximant of degree 2

  L2 data approximation error = 0.0473605

  Normalized length of piecewise linear interpolant = 2.68209
  Normalized length of polynomial approximant       = 1.2402
  Created plot file "p06_poly02.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #6.
  Number of data points = 49

  Data array:

  Row:       1             2       
  Col
    1:  595.000000    0.644000
    2:  605.000000    0.622000
    3:  615.000000    0.638000
    4:  625.000000    0.649000
    5:  635.000000    0.652000
    6:  645.000000    0.639000
    7:  655.000000    0.646000
    8:  665.000000    0.657000
    9:  675.000000    0.652000
   10:  685.000000    0.655000
   11:  695.000000    0.644000
   12:  705.000000    0.663000
   13:  715.000000    0.663000
   14:  725.000000    0.668000
   15:  735.000000    0.676000
   16:  745.000000    0.676000
   17:  755.000000    0.686000
   18:  765.000000    0.679000
   19:  775.000000    0.678000
   20:  785.000000    0.683000
   21:  795.000000    0.694000
   22:  805.000000    0.699000
   23:  815.000000    0.710000
   24:  825.000000    0.730000
   25:  835.000000    0.763000
   26:  845.000000    0.812000
   27:  855.000000    0.907000
   28:  865.000000    1.044000
   29:  875.000000    1.336000
   30:  885.000000    1.881000
   31:  895.000000    2.169000
   32:  905.000000    2.075000
   33:  915.000000    1.598000
   34:  925.000000    1.211000
   35:  935.000000    0.916000
   36:  945.000000    0.746000
   37:  955.000000    0.672000
   38:  965.000000    0.627000
   39:  975.000000    0.615000
   40:  985.000000    0.607000
   41:  995.000000    0.606000
   42: 1005.000000    0.609000
   43: 1015.000000    0.603000
   44: 1025.000000    0.601000
   45: 1035.000000    0.603000
   46: 1045.000000    0.601000
   47: 1055.000000    0.611000
   48: 1065.000000    0.601000
   49: 1075.000000    0.608000
  Using polynomial approximant of degree 3

  L2 data approximation error = 0.0437687

  Normalized length of piecewise linear interpolant = 2.68209
  Normalized length of polynomial approximant       = 1.43902
  Created plot file "p06_poly03.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #6.
  Number of data points = 49

  Data array:

  Row:       1             2       
  Col
    1:  595.000000    0.644000
    2:  605.000000    0.622000
    3:  615.000000    0.638000
    4:  625.000000    0.649000
    5:  635.000000    0.652000
    6:  645.000000    0.639000
    7:  655.000000    0.646000
    8:  665.000000    0.657000
    9:  675.000000    0.652000
   10:  685.000000    0.655000
   11:  695.000000    0.644000
   12:  705.000000    0.663000
   13:  715.000000    0.663000
   14:  725.000000    0.668000
   15:  735.000000    0.676000
   16:  745.000000    0.676000
   17:  755.000000    0.686000
   18:  765.000000    0.679000
   19:  775.000000    0.678000
   20:  785.000000    0.683000
   21:  795.000000    0.694000
   22:  805.000000    0.699000
   23:  815.000000    0.710000
   24:  825.000000    0.730000
   25:  835.000000    0.763000
   26:  845.000000    0.812000
   27:  855.000000    0.907000
   28:  865.000000    1.044000
   29:  875.000000    1.336000
   30:  885.000000    1.881000
   31:  895.000000    2.169000
   32:  905.000000    2.075000
   33:  915.000000    1.598000
   34:  925.000000    1.211000
   35:  935.000000    0.916000
   36:  945.000000    0.746000
   37:  955.000000    0.672000
   38:  965.000000    0.627000
   39:  975.000000    0.615000
   40:  985.000000    0.607000
   41:  995.000000    0.606000
   42: 1005.000000    0.609000
   43: 1015.000000    0.603000
   44: 1025.000000    0.601000
   45: 1035.000000    0.603000
   46: 1045.000000    0.601000
   47: 1055.000000    0.611000
   48: 1065.000000    0.601000
   49: 1075.000000    0.608000
  Using polynomial approximant of degree 4
[Warning: Rank deficient, rank = 4, tol =  5.115918e-02.] 
[> In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('vandermonde_approx_1d_test01', '/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test01.m', 47)" style="font-weight:bold">vandermonde_approx_1d_test01</a> (<a href="matlab: opentoline('/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test01.m',47,0)">line 47</a>)
  In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('vandermonde_approx_1d_test', '/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test.m', 32)" style="font-weight:bold">vandermonde_approx_1d_test</a> (<a href="matlab: opentoline('/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test.m',32,0)">line 32</a>)
] 

  L2 data approximation error = 0.0443293

  Normalized length of piecewise linear interpolant = 2.68209
  Normalized length of polynomial approximant       = 1.41035
  Created plot file "p06_poly04.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #6.
  Number of data points = 49

  Data array:

  Row:       1             2       
  Col
    1:  595.000000    0.644000
    2:  605.000000    0.622000
    3:  615.000000    0.638000
    4:  625.000000    0.649000
    5:  635.000000    0.652000
    6:  645.000000    0.639000
    7:  655.000000    0.646000
    8:  665.000000    0.657000
    9:  675.000000    0.652000
   10:  685.000000    0.655000
   11:  695.000000    0.644000
   12:  705.000000    0.663000
   13:  715.000000    0.663000
   14:  725.000000    0.668000
   15:  735.000000    0.676000
   16:  745.000000    0.676000
   17:  755.000000    0.686000
   18:  765.000000    0.679000
   19:  775.000000    0.678000
   20:  785.000000    0.683000
   21:  795.000000    0.694000
   22:  805.000000    0.699000
   23:  815.000000    0.710000
   24:  825.000000    0.730000
   25:  835.000000    0.763000
   26:  845.000000    0.812000
   27:  855.000000    0.907000
   28:  865.000000    1.044000
   29:  875.000000    1.336000
   30:  885.000000    1.881000
   31:  895.000000    2.169000
   32:  905.000000    2.075000
   33:  915.000000    1.598000
   34:  925.000000    1.211000
   35:  935.000000    0.916000
   36:  945.000000    0.746000
   37:  955.000000    0.672000
   38:  965.000000    0.627000
   39:  975.000000    0.615000
   40:  985.000000    0.607000
   41:  995.000000    0.606000
   42: 1005.000000    0.609000
   43: 1015.000000    0.603000
   44: 1025.000000    0.601000
   45: 1035.000000    0.603000
   46: 1045.000000    0.601000
   47: 1055.000000    0.611000
   48: 1065.000000    0.601000
   49: 1075.000000    0.608000
  Using polynomial approximant of degree 5
[Warning: Rank deficient, rank = 4, tol =  5.005005e+01.] 
[> In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('vandermonde_approx_1d_test01', '/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test01.m', 47)" style="font-weight:bold">vandermonde_approx_1d_test01</a> (<a href="matlab: opentoline('/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test01.m',47,0)">line 47</a>)
  In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('vandermonde_approx_1d_test', '/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test.m', 32)" style="font-weight:bold">vandermonde_approx_1d_test</a> (<a href="matlab: opentoline('/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test.m',32,0)">line 32</a>)
] 

  L2 data approximation error = 0.0448312

  Normalized length of piecewise linear interpolant = 2.68209
  Normalized length of polynomial approximant       = 1.39049
  Created plot file "p06_poly05.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #6.
  Number of data points = 49

  Data array:

  Row:       1             2       
  Col
    1:  595.000000    0.644000
    2:  605.000000    0.622000
    3:  615.000000    0.638000
    4:  625.000000    0.649000
    5:  635.000000    0.652000
    6:  645.000000    0.639000
    7:  655.000000    0.646000
    8:  665.000000    0.657000
    9:  675.000000    0.652000
   10:  685.000000    0.655000
   11:  695.000000    0.644000
   12:  705.000000    0.663000
   13:  715.000000    0.663000
   14:  725.000000    0.668000
   15:  735.000000    0.676000
   16:  745.000000    0.676000
   17:  755.000000    0.686000
   18:  765.000000    0.679000
   19:  775.000000    0.678000
   20:  785.000000    0.683000
   21:  795.000000    0.694000
   22:  805.000000    0.699000
   23:  815.000000    0.710000
   24:  825.000000    0.730000
   25:  835.000000    0.763000
   26:  845.000000    0.812000
   27:  855.000000    0.907000
   28:  865.000000    1.044000
   29:  875.000000    1.336000
   30:  885.000000    1.881000
   31:  895.000000    2.169000
   32:  905.000000    2.075000
   33:  915.000000    1.598000
   34:  925.000000    1.211000
   35:  935.000000    0.916000
   36:  945.000000    0.746000
   37:  955.000000    0.672000
   38:  965.000000    0.627000
   39:  975.000000    0.615000
   40:  985.000000    0.607000
   41:  995.000000    0.606000
   42: 1005.000000    0.609000
   43: 1015.000000    0.603000
   44: 1025.000000    0.601000
   45: 1035.000000    0.603000
   46: 1045.000000    0.601000
   47: 1055.000000    0.611000
   48: 1065.000000    0.601000
   49: 1075.000000    0.608000
  Using polynomial approximant of degree 9
[Warning: Rank deficient, rank = 4, tol =  5.182242e+13.] 
[> In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('vandermonde_approx_1d_test01', '/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test01.m', 47)" style="font-weight:bold">vandermonde_approx_1d_test01</a> (<a href="matlab: opentoline('/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test01.m',47,0)">line 47</a>)
  In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('vandermonde_approx_1d_test', '/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test.m', 32)" style="font-weight:bold">vandermonde_approx_1d_test</a> (<a href="matlab: opentoline('/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test.m',32,0)">line 32</a>)
] 

  L2 data approximation error = 0.0447827

  Normalized length of piecewise linear interpolant = 2.68209
  Normalized length of polynomial approximant       = 1.35233
  Created plot file "p06_poly09.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #6.
  Number of data points = 49

  Data array:

  Row:       1             2       
  Col
    1:  595.000000    0.644000
    2:  605.000000    0.622000
    3:  615.000000    0.638000
    4:  625.000000    0.649000
    5:  635.000000    0.652000
    6:  645.000000    0.639000
    7:  655.000000    0.646000
    8:  665.000000    0.657000
    9:  675.000000    0.652000
   10:  685.000000    0.655000
   11:  695.000000    0.644000
   12:  705.000000    0.663000
   13:  715.000000    0.663000
   14:  725.000000    0.668000
   15:  735.000000    0.676000
   16:  745.000000    0.676000
   17:  755.000000    0.686000
   18:  765.000000    0.679000
   19:  775.000000    0.678000
   20:  785.000000    0.683000
   21:  795.000000    0.694000
   22:  805.000000    0.699000
   23:  815.000000    0.710000
   24:  825.000000    0.730000
   25:  835.000000    0.763000
   26:  845.000000    0.812000
   27:  855.000000    0.907000
   28:  865.000000    1.044000
   29:  875.000000    1.336000
   30:  885.000000    1.881000
   31:  895.000000    2.169000
   32:  905.000000    2.075000
   33:  915.000000    1.598000
   34:  925.000000    1.211000
   35:  935.000000    0.916000
   36:  945.000000    0.746000
   37:  955.000000    0.672000
   38:  965.000000    0.627000
   39:  975.000000    0.615000
   40:  985.000000    0.607000
   41:  995.000000    0.606000
   42: 1005.000000    0.609000
   43: 1015.000000    0.603000
   44: 1025.000000    0.601000
   45: 1035.000000    0.603000
   46: 1045.000000    0.601000
   47: 1055.000000    0.611000
   48: 1065.000000    0.601000
   49: 1075.000000    0.608000
  Using polynomial approximant of degree 12
[Warning: Rank deficient, rank = 4, tol =  5.688501e+22.] 
[> In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('vandermonde_approx_1d_test01', '/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test01.m', 47)" style="font-weight:bold">vandermonde_approx_1d_test01</a> (<a href="matlab: opentoline('/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test01.m',47,0)">line 47</a>)
  In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('vandermonde_approx_1d_test', '/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test.m', 32)" style="font-weight:bold">vandermonde_approx_1d_test</a> (<a href="matlab: opentoline('/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test.m',32,0)">line 32</a>)
] 

  L2 data approximation error = 0.0449233

  Normalized length of piecewise linear interpolant = 2.68209
  Normalized length of polynomial approximant       = 1.52582
  Created plot file "p06_poly12.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #7.
  Number of data points = 4

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    1.000000
    2:    1.000000    2.000000
    3:    4.000000    2.000000
    4:    5.000000    1.000000
  Using polynomial approximant of degree 0

  L2 data approximation error = 0.25

  Normalized length of piecewise linear interpolant = 2.63961
  Normalized length of polynomial approximant       = 1
  Created plot file "p07_poly00.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #7.
  Number of data points = 4

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    1.000000
    2:    1.000000    2.000000
    3:    4.000000    2.000000
    4:    5.000000    1.000000
  Using polynomial approximant of degree 1

  L2 data approximation error = 0.25

  Normalized length of piecewise linear interpolant = 2.63961
  Normalized length of polynomial approximant       = 1

  Created plot file "p07_data.png".
  Created plot file "p07_poly01.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #7.
  Number of data points = 4

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    1.000000
    2:    1.000000    2.000000
    3:    4.000000    2.000000
    4:    5.000000    1.000000
  Using polynomial approximant of degree 2

  L2 data approximation error = 8.00593e-16

  Normalized length of piecewise linear interpolant = 2.63961
  Normalized length of polynomial approximant       = 3.36731
  Created plot file "p07_poly02.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #7.
  Number of data points = 4

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    1.000000
    2:    1.000000    2.000000
    3:    4.000000    2.000000
    4:    5.000000    1.000000
  Using polynomial approximant of degree 3

  L2 data approximation error = 2.77556e-16

  Normalized length of piecewise linear interpolant = 2.63961
  Normalized length of polynomial approximant       = 3.36731
  Created plot file "p07_poly03.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #7.
  Number of data points = 4

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    1.000000
    2:    1.000000    2.000000
    3:    4.000000    2.000000
    4:    5.000000    1.000000
  Using polynomial approximant of degree 4

  L2 data approximation error = 3.59753e-16

  Normalized length of piecewise linear interpolant = 2.63961
  Normalized length of polynomial approximant       = 3.58258
  Created plot file "p07_poly04.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #7.
  Number of data points = 4

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    1.000000
    2:    1.000000    2.000000
    3:    4.000000    2.000000
    4:    5.000000    1.000000
  Using polynomial approximant of degree 5

  L2 data approximation error = 5.02675e-16

  Normalized length of piecewise linear interpolant = 2.63961
  Normalized length of polynomial approximant       = 3.90825
  Created plot file "p07_poly05.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #7.
  Number of data points = 4

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    1.000000
    2:    1.000000    2.000000
    3:    4.000000    2.000000
    4:    5.000000    1.000000
  Using polynomial approximant of degree 9

  L2 data approximation error = 4.2119e-15

  Normalized length of piecewise linear interpolant = 2.63961
  Normalized length of polynomial approximant       = 6.52763
  Created plot file "p07_poly09.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #7.
  Number of data points = 4

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    1.000000
    2:    1.000000    2.000000
    3:    4.000000    2.000000
    4:    5.000000    1.000000
  Using polynomial approximant of degree 12

  L2 data approximation error = 2.44816e-15

  Normalized length of piecewise linear interpolant = 2.63961
  Normalized length of polynomial approximant       = 10.4248
  Created plot file "p07_poly12.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #8.
  Number of data points = 12

  Data array:

  Row:       1             2       
  Col
    1:   -1.000000    1.000000
    2:   -0.800000    0.640000
    3:   -0.600000    0.360000
    4:   -0.400000    0.160000
    5:   -0.200000    0.040000
    6:    0.000000    0.000000
    7:    0.200000    0.040000
    8:    0.200010    0.050000
    9:    0.400000    0.160000
   10:    0.600000    0.360000
   11:    0.800000    0.640000
   12:    1.000000    1.000000
  Using polynomial approximant of degree 0

  L2 data approximation error = 0.101554

  Normalized length of piecewise linear interpolant = 2.31939
  Normalized length of polynomial approximant       = 1
  Created plot file "p08_poly00.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #8.
  Number of data points = 12

  Data array:

  Row:       1             2       
  Col
    1:   -1.000000    1.000000
    2:   -0.800000    0.640000
    3:   -0.600000    0.360000
    4:   -0.400000    0.160000
    5:   -0.200000    0.040000
    6:    0.000000    0.000000
    7:    0.200000    0.040000
    8:    0.200010    0.050000
    9:    0.400000    0.160000
   10:    0.600000    0.360000
   11:    0.800000    0.640000
   12:    1.000000    1.000000
  Using polynomial approximant of degree 1

  L2 data approximation error = 0.101522

  Normalized length of piecewise linear interpolant = 2.31939
  Normalized length of polynomial approximant       = 1.00042

  Created plot file "p08_data.png".
  Created plot file "p08_poly01.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #8.
  Number of data points = 12

  Data array:

  Row:       1             2       
  Col
    1:   -1.000000    1.000000
    2:   -0.800000    0.640000
    3:   -0.600000    0.360000
    4:   -0.400000    0.160000
    5:   -0.200000    0.040000
    6:    0.000000    0.000000
    7:    0.200000    0.040000
    8:    0.200010    0.050000
    9:    0.400000    0.160000
   10:    0.600000    0.360000
   11:    0.800000    0.640000
   12:    1.000000    1.000000
  Using polynomial approximant of degree 2

  L2 data approximation error = 0.000762201

  Normalized length of piecewise linear interpolant = 2.31939
  Normalized length of polynomial approximant       = 2.31944
  Created plot file "p08_poly02.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #8.
  Number of data points = 12

  Data array:

  Row:       1             2       
  Col
    1:   -1.000000    1.000000
    2:   -0.800000    0.640000
    3:   -0.600000    0.360000
    4:   -0.400000    0.160000
    5:   -0.200000    0.040000
    6:    0.000000    0.000000
    7:    0.200000    0.040000
    8:    0.200010    0.050000
    9:    0.400000    0.160000
   10:    0.600000    0.360000
   11:    0.800000    0.640000
   12:    1.000000    1.000000
  Using polynomial approximant of degree 3

  L2 data approximation error = 0.000748027

  Normalized length of piecewise linear interpolant = 2.31939
  Normalized length of polynomial approximant       = 2.31959
  Created plot file "p08_poly03.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #8.
  Number of data points = 12

  Data array:

  Row:       1             2       
  Col
    1:   -1.000000    1.000000
    2:   -0.800000    0.640000
    3:   -0.600000    0.360000
    4:   -0.400000    0.160000
    5:   -0.200000    0.040000
    6:    0.000000    0.000000
    7:    0.200000    0.040000
    8:    0.200010    0.050000
    9:    0.400000    0.160000
   10:    0.600000    0.360000
   11:    0.800000    0.640000
   12:    1.000000    1.000000
  Using polynomial approximant of degree 4

  L2 data approximation error = 0.000731706

  Normalized length of piecewise linear interpolant = 2.31939
  Normalized length of polynomial approximant       = 2.32028
  Created plot file "p08_poly04.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #8.
  Number of data points = 12

  Data array:

  Row:       1             2       
  Col
    1:   -1.000000    1.000000
    2:   -0.800000    0.640000
    3:   -0.600000    0.360000
    4:   -0.400000    0.160000
    5:   -0.200000    0.040000
    6:    0.000000    0.000000
    7:    0.200000    0.040000
    8:    0.200010    0.050000
    9:    0.400000    0.160000
   10:    0.600000    0.360000
   11:    0.800000    0.640000
   12:    1.000000    1.000000
  Using polynomial approximant of degree 5

  L2 data approximation error = 0.000704364

  Normalized length of piecewise linear interpolant = 2.31939
  Normalized length of polynomial approximant       = 2.32052
  Created plot file "p08_poly05.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #8.
  Number of data points = 12

  Data array:

  Row:       1             2       
  Col
    1:   -1.000000    1.000000
    2:   -0.800000    0.640000
    3:   -0.600000    0.360000
    4:   -0.400000    0.160000
    5:   -0.200000    0.040000
    6:    0.000000    0.000000
    7:    0.200000    0.040000
    8:    0.200010    0.050000
    9:    0.400000    0.160000
   10:    0.600000    0.360000
   11:    0.800000    0.640000
   12:    1.000000    1.000000
  Using polynomial approximant of degree 9

  L2 data approximation error = 0.000627667

  Normalized length of piecewise linear interpolant = 2.31939
  Normalized length of polynomial approximant       = 2.32096
  Created plot file "p08_poly09.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #8.
  Number of data points = 12

  Data array:

  Row:       1             2       
  Col
    1:   -1.000000    1.000000
    2:   -0.800000    0.640000
    3:   -0.600000    0.360000
    4:   -0.400000    0.160000
    5:   -0.200000    0.040000
    6:    0.000000    0.000000
    7:    0.200000    0.040000
    8:    0.200010    0.050000
    9:    0.400000    0.160000
   10:    0.600000    0.360000
   11:    0.800000    0.640000
   12:    1.000000    1.000000
  Using polynomial approximant of degree 12

  L2 data approximation error = 4.23538e-11

  Normalized length of piecewise linear interpolant = 2.31939
  Normalized length of polynomial approximant       = 23167
  Created plot file "p08_poly12.png".

vandermonde_approx_1d_test:
  Normal end of execution.

18-Feb-2019 20:32:29
vandermonde_approx_1d_test
18-Feb-2019 20:34:51

vandermonde_approx_1d_test:
  MATLAB version
  Test vandermonde_approx_1d.

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #1.
  Number of data points = 18

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    4.000000
    2:    1.000000    5.000000
    3:    2.000000    6.000000
    4:    4.000000    6.000000
    5:    5.000000    5.000000
    6:    6.000000    3.000000
    7:    7.000000    1.000000
    8:    8.000000    1.000000
    9:    9.000000    1.000000
   10:   10.000000    3.000000
   11:   11.000000    4.000000
   12:   12.000000    4.000000
   13:   13.000000    3.000000
   14:   14.000000    3.000000
   15:   15.000000    4.000000
   16:   16.000000    4.000000
   17:   17.000000    3.000000
   18:   18.000000    0.000000
  Using polynomial approximant of degree 0
{Undefined function or variable 'r8poly_values_horner_fast'.

Error in <a href="matlab:matlab.internal.language.introspective.errorDocCallback('vandermonde_approx_1d_test01', '/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test01.m', 53)" style="font-weight:bold">vandermonde_approx_1d_test01</a> (<a href="matlab: opentoline('/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test01.m',53,0)">line 53</a>)
  yi = r8poly_values_horner_fast ( m, c, ni, xi );

Error in <a href="matlab:matlab.internal.language.introspective.errorDocCallback('vandermonde_approx_1d_test', '/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test.m', 32)" style="font-weight:bold">vandermonde_approx_1d_test</a> (<a href="matlab: opentoline('/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test.m',32,0)">line 32</a>)
      vandermonde_approx_1d_test01 ( prob, m );
} 
vandermonde_approx_1d_test
18-Feb-2019 20:35:41

vandermonde_approx_1d_test:
  MATLAB version
  Test vandermonde_approx_1d.

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #1.
  Number of data points = 18

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    4.000000
    2:    1.000000    5.000000
    3:    2.000000    6.000000
    4:    4.000000    6.000000
    5:    5.000000    5.000000
    6:    6.000000    3.000000
    7:    7.000000    1.000000
    8:    8.000000    1.000000
    9:    9.000000    1.000000
   10:   10.000000    3.000000
   11:   11.000000    4.000000
   12:   12.000000    4.000000
   13:   13.000000    3.000000
   14:   14.000000    3.000000
   15:   15.000000    4.000000
   16:   16.000000    4.000000
   17:   17.000000    3.000000
   18:   18.000000    0.000000
  Using polynomial approximant of degree 0

  L2 data approximation error = 0.392837
{Undefined function or variable 'r8poly_values_horner_fast'.

Error in <a href="matlab:matlab.internal.language.introspective.errorDocCallback('vandermonde_approx_1d_test01', '/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test01.m', 71)" style="font-weight:bold">vandermonde_approx_1d_test01</a> (<a href="matlab: opentoline('/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test01.m',71,0)">line 71</a>)
  yi = r8poly_values_horner_fast ( m, c, ni, xi );

Error in <a href="matlab:matlab.internal.language.introspective.errorDocCallback('vandermonde_approx_1d_test', '/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test.m', 32)" style="font-weight:bold">vandermonde_approx_1d_test</a> (<a href="matlab: opentoline('/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test.m',32,0)">line 32</a>)
      vandermonde_approx_1d_test01 ( prob, m );
} 
vandermonde_approx_1d_test
18-Feb-2019 20:35:58

vandermonde_approx_1d_test:
  MATLAB version
  Test vandermonde_approx_1d.

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #1.
  Number of data points = 18

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    4.000000
    2:    1.000000    5.000000
    3:    2.000000    6.000000
    4:    4.000000    6.000000
    5:    5.000000    5.000000
    6:    6.000000    3.000000
    7:    7.000000    1.000000
    8:    8.000000    1.000000
    9:    9.000000    1.000000
   10:   10.000000    3.000000
   11:   11.000000    4.000000
   12:   12.000000    4.000000
   13:   13.000000    3.000000
   14:   14.000000    3.000000
   15:   15.000000    4.000000
   16:   16.000000    4.000000
   17:   17.000000    3.000000
   18:   18.000000    0.000000
  Using polynomial approximant of degree 0

  L2 data approximation error = 0.392837

  Normalized length of piecewise linear interpolant = 3.13553
  Normalized length of polynomial approximant       = 1
  Created plot file "p01_poly00.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #1.
  Number of data points = 18

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    4.000000
    2:    1.000000    5.000000
    3:    2.000000    6.000000
    4:    4.000000    6.000000
    5:    5.000000    5.000000
    6:    6.000000    3.000000
    7:    7.000000    1.000000
    8:    8.000000    1.000000
    9:    9.000000    1.000000
   10:   10.000000    3.000000
   11:   11.000000    4.000000
   12:   12.000000    4.000000
   13:   13.000000    3.000000
   14:   14.000000    3.000000
   15:   15.000000    4.000000
   16:   16.000000    4.000000
   17:   17.000000    3.000000
   18:   18.000000    0.000000
  Using polynomial approximant of degree 1

  L2 data approximation error = 0.350074

  Normalized length of piecewise linear interpolant = 3.13553
  Normalized length of polynomial approximant       = 1.08357

  Created plot file "p01_data.png".
  Created plot file "p01_poly01.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #1.
  Number of data points = 18

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    4.000000
    2:    1.000000    5.000000
    3:    2.000000    6.000000
    4:    4.000000    6.000000
    5:    5.000000    5.000000
    6:    6.000000    3.000000
    7:    7.000000    1.000000
    8:    8.000000    1.000000
    9:    9.000000    1.000000
   10:   10.000000    3.000000
   11:   11.000000    4.000000
   12:   12.000000    4.000000
   13:   13.000000    3.000000
   14:   14.000000    3.000000
   15:   15.000000    4.000000
   16:   16.000000    4.000000
   17:   17.000000    3.000000
   18:   18.000000    0.000000
  Using polynomial approximant of degree 2

  L2 data approximation error = 0.344057

  Normalized length of piecewise linear interpolant = 3.13553
  Normalized length of polynomial approximant       = 1.12211
  Created plot file "p01_poly02.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #1.
  Number of data points = 18

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    4.000000
    2:    1.000000    5.000000
    3:    2.000000    6.000000
    4:    4.000000    6.000000
    5:    5.000000    5.000000
    6:    6.000000    3.000000
    7:    7.000000    1.000000
    8:    8.000000    1.000000
    9:    9.000000    1.000000
   10:   10.000000    3.000000
   11:   11.000000    4.000000
   12:   12.000000    4.000000
   13:   13.000000    3.000000
   14:   14.000000    3.000000
   15:   15.000000    4.000000
   16:   16.000000    4.000000
   17:   17.000000    3.000000
   18:   18.000000    0.000000
  Using polynomial approximant of degree 3

  L2 data approximation error = 0.332868

  Normalized length of piecewise linear interpolant = 3.13553
  Normalized length of polynomial approximant       = 1.31026
  Created plot file "p01_poly03.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #1.
  Number of data points = 18

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    4.000000
    2:    1.000000    5.000000
    3:    2.000000    6.000000
    4:    4.000000    6.000000
    5:    5.000000    5.000000
    6:    6.000000    3.000000
    7:    7.000000    1.000000
    8:    8.000000    1.000000
    9:    9.000000    1.000000
   10:   10.000000    3.000000
   11:   11.000000    4.000000
   12:   12.000000    4.000000
   13:   13.000000    3.000000
   14:   14.000000    3.000000
   15:   15.000000    4.000000
   16:   16.000000    4.000000
   17:   17.000000    3.000000
   18:   18.000000    0.000000
  Using polynomial approximant of degree 4

  L2 data approximation error = 0.199123

  Normalized length of piecewise linear interpolant = 3.13553
  Normalized length of polynomial approximant       = 2.51647
  Created plot file "p01_poly04.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #1.
  Number of data points = 18

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    4.000000
    2:    1.000000    5.000000
    3:    2.000000    6.000000
    4:    4.000000    6.000000
    5:    5.000000    5.000000
    6:    6.000000    3.000000
    7:    7.000000    1.000000
    8:    8.000000    1.000000
    9:    9.000000    1.000000
   10:   10.000000    3.000000
   11:   11.000000    4.000000
   12:   12.000000    4.000000
   13:   13.000000    3.000000
   14:   14.000000    3.000000
   15:   15.000000    4.000000
   16:   16.000000    4.000000
   17:   17.000000    3.000000
   18:   18.000000    0.000000
  Using polynomial approximant of degree 5

  L2 data approximation error = 0.190907

  Normalized length of piecewise linear interpolant = 3.13553
  Normalized length of polynomial approximant       = 2.60932
  Created plot file "p01_poly05.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #1.
  Number of data points = 18

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    4.000000
    2:    1.000000    5.000000
    3:    2.000000    6.000000
    4:    4.000000    6.000000
    5:    5.000000    5.000000
    6:    6.000000    3.000000
    7:    7.000000    1.000000
    8:    8.000000    1.000000
    9:    9.000000    1.000000
   10:   10.000000    3.000000
   11:   11.000000    4.000000
   12:   12.000000    4.000000
   13:   13.000000    3.000000
   14:   14.000000    3.000000
   15:   15.000000    4.000000
   16:   16.000000    4.000000
   17:   17.000000    3.000000
   18:   18.000000    0.000000
  Using polynomial approximant of degree 9

  L2 data approximation error = 0.0613776

  Normalized length of piecewise linear interpolant = 3.13553
  Normalized length of polynomial approximant       = 3.22044
  Created plot file "p01_poly09.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #1.
  Number of data points = 18

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    4.000000
    2:    1.000000    5.000000
    3:    2.000000    6.000000
    4:    4.000000    6.000000
    5:    5.000000    5.000000
    6:    6.000000    3.000000
    7:    7.000000    1.000000
    8:    8.000000    1.000000
    9:    9.000000    1.000000
   10:   10.000000    3.000000
   11:   11.000000    4.000000
   12:   12.000000    4.000000
   13:   13.000000    3.000000
   14:   14.000000    3.000000
   15:   15.000000    4.000000
   16:   16.000000    4.000000
   17:   17.000000    3.000000
   18:   18.000000    0.000000
  Using polynomial approximant of degree 12
[Warning: Rank deficient, rank = 8, tol =  5.328830e+00.] 
[> In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('vandermonde_approx_1d_test01', '/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test01.m', 47)" style="font-weight:bold">vandermonde_approx_1d_test01</a> (<a href="matlab: opentoline('/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test01.m',47,0)">line 47</a>)
  In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('vandermonde_approx_1d_test', '/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test.m', 32)" style="font-weight:bold">vandermonde_approx_1d_test</a> (<a href="matlab: opentoline('/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test.m',32,0)">line 32</a>)
] 

  L2 data approximation error = 0.465929

  Normalized length of piecewise linear interpolant = 3.13553
  Normalized length of polynomial approximant       = 4.39868
  Created plot file "p01_poly12.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #2.
  Number of data points = 18

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    1.340000    5.000000
    3:    5.000000    8.660000
    4:   10.000000   10.000000
    5:   10.600000   10.400000
    6:   10.700000   12.000000
    7:   10.705000   28.600000
    8:   10.800000   30.200000
    9:   11.400000   30.600000
   10:   19.600000   30.600000
   11:   20.200000   30.200000
   12:   20.295000   28.600000
   13:   20.300000   12.000000
   14:   20.400000   10.400000
   15:   21.000000   10.000000
   16:   26.000000    8.660000
   17:   29.660000    5.000000
   18:   31.000000    0.000000
  Using polynomial approximant of degree 0

  L2 data approximation error = 2.58162

  Normalized length of piecewise linear interpolant = 2.66086
  Normalized length of polynomial approximant       = 1
  Created plot file "p02_poly00.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #2.
  Number of data points = 18

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    1.340000    5.000000
    3:    5.000000    8.660000
    4:   10.000000   10.000000
    5:   10.600000   10.400000
    6:   10.700000   12.000000
    7:   10.705000   28.600000
    8:   10.800000   30.200000
    9:   11.400000   30.600000
   10:   19.600000   30.600000
   11:   20.200000   30.200000
   12:   20.295000   28.600000
   13:   20.300000   12.000000
   14:   20.400000   10.400000
   15:   21.000000   10.000000
   16:   26.000000    8.660000
   17:   29.660000    5.000000
   18:   31.000000    0.000000
  Using polynomial approximant of degree 1

  L2 data approximation error = 2.58162

  Normalized length of piecewise linear interpolant = 2.66086
  Normalized length of polynomial approximant       = 1

  Created plot file "p02_data.png".
  Created plot file "p02_poly01.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #2.
  Number of data points = 18

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    1.340000    5.000000
    3:    5.000000    8.660000
    4:   10.000000   10.000000
    5:   10.600000   10.400000
    6:   10.700000   12.000000
    7:   10.705000   28.600000
    8:   10.800000   30.200000
    9:   11.400000   30.600000
   10:   19.600000   30.600000
   11:   20.200000   30.200000
   12:   20.295000   28.600000
   13:   20.300000   12.000000
   14:   20.400000   10.400000
   15:   21.000000   10.000000
   16:   26.000000    8.660000
   17:   29.660000    5.000000
   18:   31.000000    0.000000
  Using polynomial approximant of degree 2

  L2 data approximation error = 1.80946

  Normalized length of piecewise linear interpolant = 2.66086
  Normalized length of polynomial approximant       = 1.88131
  Created plot file "p02_poly02.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #2.
  Number of data points = 18

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    1.340000    5.000000
    3:    5.000000    8.660000
    4:   10.000000   10.000000
    5:   10.600000   10.400000
    6:   10.700000   12.000000
    7:   10.705000   28.600000
    8:   10.800000   30.200000
    9:   11.400000   30.600000
   10:   19.600000   30.600000
   11:   20.200000   30.200000
   12:   20.295000   28.600000
   13:   20.300000   12.000000
   14:   20.400000   10.400000
   15:   21.000000   10.000000
   16:   26.000000    8.660000
   17:   29.660000    5.000000
   18:   31.000000    0.000000
  Using polynomial approximant of degree 3

  L2 data approximation error = 1.80946

  Normalized length of piecewise linear interpolant = 2.66086
  Normalized length of polynomial approximant       = 1.88131
  Created plot file "p02_poly03.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #2.
  Number of data points = 18

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    1.340000    5.000000
    3:    5.000000    8.660000
    4:   10.000000   10.000000
    5:   10.600000   10.400000
    6:   10.700000   12.000000
    7:   10.705000   28.600000
    8:   10.800000   30.200000
    9:   11.400000   30.600000
   10:   19.600000   30.600000
   11:   20.200000   30.200000
   12:   20.295000   28.600000
   13:   20.300000   12.000000
   14:   20.400000   10.400000
   15:   21.000000   10.000000
   16:   26.000000    8.660000
   17:   29.660000    5.000000
   18:   31.000000    0.000000
  Using polynomial approximant of degree 4

  L2 data approximation error = 1.76341

  Normalized length of piecewise linear interpolant = 2.66086
  Normalized length of polynomial approximant       = 1.90124
  Created plot file "p02_poly04.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #2.
  Number of data points = 18

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    1.340000    5.000000
    3:    5.000000    8.660000
    4:   10.000000   10.000000
    5:   10.600000   10.400000
    6:   10.700000   12.000000
    7:   10.705000   28.600000
    8:   10.800000   30.200000
    9:   11.400000   30.600000
   10:   19.600000   30.600000
   11:   20.200000   30.200000
   12:   20.295000   28.600000
   13:   20.300000   12.000000
   14:   20.400000   10.400000
   15:   21.000000   10.000000
   16:   26.000000    8.660000
   17:   29.660000    5.000000
   18:   31.000000    0.000000
  Using polynomial approximant of degree 5

  L2 data approximation error = 1.76341

  Normalized length of piecewise linear interpolant = 2.66086
  Normalized length of polynomial approximant       = 1.90124
  Created plot file "p02_poly05.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #2.
  Number of data points = 18

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    1.340000    5.000000
    3:    5.000000    8.660000
    4:   10.000000   10.000000
    5:   10.600000   10.400000
    6:   10.700000   12.000000
    7:   10.705000   28.600000
    8:   10.800000   30.200000
    9:   11.400000   30.600000
   10:   19.600000   30.600000
   11:   20.200000   30.200000
   12:   20.295000   28.600000
   13:   20.300000   12.000000
   14:   20.400000   10.400000
   15:   21.000000   10.000000
   16:   26.000000    8.660000
   17:   29.660000    5.000000
   18:   31.000000    0.000000
  Using polynomial approximant of degree 9

  L2 data approximation error = 1.30404

  Normalized length of piecewise linear interpolant = 2.66086
  Normalized length of polynomial approximant       = 8.90486
  Created plot file "p02_poly09.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #2.
  Number of data points = 18

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    1.340000    5.000000
    3:    5.000000    8.660000
    4:   10.000000   10.000000
    5:   10.600000   10.400000
    6:   10.700000   12.000000
    7:   10.705000   28.600000
    8:   10.800000   30.200000
    9:   11.400000   30.600000
   10:   19.600000   30.600000
   11:   20.200000   30.200000
   12:   20.295000   28.600000
   13:   20.300000   12.000000
   14:   20.400000   10.400000
   15:   21.000000   10.000000
   16:   26.000000    8.660000
   17:   29.660000    5.000000
   18:   31.000000    0.000000
  Using polynomial approximant of degree 12
[Warning: Rank deficient, rank = 7, tol =  3.672964e+03.] 
[> In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('vandermonde_approx_1d_test01', '/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test01.m', 47)" style="font-weight:bold">vandermonde_approx_1d_test01</a> (<a href="matlab: opentoline('/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test01.m',47,0)">line 47</a>)
  In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('vandermonde_approx_1d_test', '/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test.m', 32)" style="font-weight:bold">vandermonde_approx_1d_test</a> (<a href="matlab: opentoline('/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test.m',32,0)">line 32</a>)
] 

  L2 data approximation error = 1.45992

  Normalized length of piecewise linear interpolant = 2.66086
  Normalized length of polynomial approximant       = 7.11494
  Created plot file "p02_poly12.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #3.
  Number of data points = 11

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    2.000000   10.000000
    3:    3.000000   10.000000
    4:    5.000000   10.000000
    5:    6.000000   10.000000
    6:    8.000000   10.000000
    7:    9.000000   10.500000
    8:   11.000000   15.000000
    9:   12.000000   50.000000
   10:   14.000000   60.000000
   11:   15.000000   85.000000
  Using polynomial approximant of degree 0

  L2 data approximation error = 7.87737

  Normalized length of piecewise linear interpolant = 1.68472
  Normalized length of polynomial approximant       = 1
  Created plot file "p03_poly00.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #3.
  Number of data points = 11

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    2.000000   10.000000
    3:    3.000000   10.000000
    4:    5.000000   10.000000
    5:    6.000000   10.000000
    6:    8.000000   10.000000
    7:    9.000000   10.500000
    8:   11.000000   15.000000
    9:   12.000000   50.000000
   10:   14.000000   60.000000
   11:   15.000000   85.000000
  Using polynomial approximant of degree 1

  L2 data approximation error = 4.4679

  Normalized length of piecewise linear interpolant = 1.68472
  Normalized length of polynomial approximant       = 1.28026

  Created plot file "p03_data.png".
  Created plot file "p03_poly01.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #3.
  Number of data points = 11

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    2.000000   10.000000
    3:    3.000000   10.000000
    4:    5.000000   10.000000
    5:    6.000000   10.000000
    6:    8.000000   10.000000
    7:    9.000000   10.500000
    8:   11.000000   15.000000
    9:   12.000000   50.000000
   10:   14.000000   60.000000
   11:   15.000000   85.000000
  Using polynomial approximant of degree 2

  L2 data approximation error = 2.59431

  Normalized length of piecewise linear interpolant = 1.68472
  Normalized length of polynomial approximant       = 1.48631
  Created plot file "p03_poly02.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #3.
  Number of data points = 11

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    2.000000   10.000000
    3:    3.000000   10.000000
    4:    5.000000   10.000000
    5:    6.000000   10.000000
    6:    8.000000   10.000000
    7:    9.000000   10.500000
    8:   11.000000   15.000000
    9:   12.000000   50.000000
   10:   14.000000   60.000000
   11:   15.000000   85.000000
  Using polynomial approximant of degree 3

  L2 data approximation error = 1.74627

  Normalized length of piecewise linear interpolant = 1.68472
  Normalized length of polynomial approximant       = 1.58943
  Created plot file "p03_poly03.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #3.
  Number of data points = 11

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    2.000000   10.000000
    3:    3.000000   10.000000
    4:    5.000000   10.000000
    5:    6.000000   10.000000
    6:    8.000000   10.000000
    7:    9.000000   10.500000
    8:   11.000000   15.000000
    9:   12.000000   50.000000
   10:   14.000000   60.000000
   11:   15.000000   85.000000
  Using polynomial approximant of degree 4

  L2 data approximation error = 1.68297

  Normalized length of piecewise linear interpolant = 1.68472
  Normalized length of polynomial approximant       = 1.61226
  Created plot file "p03_poly04.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #3.
  Number of data points = 11

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    2.000000   10.000000
    3:    3.000000   10.000000
    4:    5.000000   10.000000
    5:    6.000000   10.000000
    6:    8.000000   10.000000
    7:    9.000000   10.500000
    8:   11.000000   15.000000
    9:   12.000000   50.000000
   10:   14.000000   60.000000
   11:   15.000000   85.000000
  Using polynomial approximant of degree 5

  L2 data approximation error = 1.66663

  Normalized length of piecewise linear interpolant = 1.68472
  Normalized length of polynomial approximant       = 1.59507
  Created plot file "p03_poly05.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #3.
  Number of data points = 11

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    2.000000   10.000000
    3:    3.000000   10.000000
    4:    5.000000   10.000000
    5:    6.000000   10.000000
    6:    8.000000   10.000000
    7:    9.000000   10.500000
    8:   11.000000   15.000000
    9:   12.000000   50.000000
   10:   14.000000   60.000000
   11:   15.000000   85.000000
  Using polynomial approximant of degree 9

  L2 data approximation error = 0.328589

  Normalized length of piecewise linear interpolant = 1.68472
  Normalized length of polynomial approximant       = 3.28924
  Created plot file "p03_poly09.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #3.
  Number of data points = 11

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    2.000000   10.000000
    3:    3.000000   10.000000
    4:    5.000000   10.000000
    5:    6.000000   10.000000
    6:    8.000000   10.000000
    7:    9.000000   10.500000
    8:   11.000000   15.000000
    9:   12.000000   50.000000
   10:   14.000000   60.000000
   11:   15.000000   85.000000
  Using polynomial approximant of degree 12
[Warning: Rank deficient, rank = 10, tol =  4.096274e-01.] 
[> In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('vandermonde_approx_1d_test01', '/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test01.m', 47)" style="font-weight:bold">vandermonde_approx_1d_test01</a> (<a href="matlab: opentoline('/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test01.m',47,0)">line 47</a>)
  In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('vandermonde_approx_1d_test', '/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test.m', 32)" style="font-weight:bold">vandermonde_approx_1d_test</a> (<a href="matlab: opentoline('/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test.m',32,0)">line 32</a>)
] 

  L2 data approximation error = 0.205051

  Normalized length of piecewise linear interpolant = 1.68472
  Normalized length of polynomial approximant       = 4.92239
  Created plot file "p03_poly12.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #4.
  Number of data points = 8

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    0.050000    0.700000
    3:    0.100000    1.000000
    4:    0.200000    1.000000
    5:    0.800000    0.300000
    6:    0.850000    0.050000
    7:    0.900000    0.100000
    8:    1.000000    1.000000
  Using polynomial approximant of degree 0

  L2 data approximation error = 0.149984

  Normalized length of piecewise linear interpolant = 3.25908
  Normalized length of polynomial approximant       = 1
  Created plot file "p04_poly00.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #4.
  Number of data points = 8

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    0.050000    0.700000
    3:    0.100000    1.000000
    4:    0.200000    1.000000
    5:    0.800000    0.300000
    6:    0.850000    0.050000
    7:    0.900000    0.100000
    8:    1.000000    1.000000
  Using polynomial approximant of degree 1

  L2 data approximation error = 0.146011

  Normalized length of piecewise linear interpolant = 3.25908
  Normalized length of polynomial approximant       = 1.02803

  Created plot file "p04_data.png".
  Created plot file "p04_poly01.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #4.
  Number of data points = 8

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    0.050000    0.700000
    3:    0.100000    1.000000
    4:    0.200000    1.000000
    5:    0.800000    0.300000
    6:    0.850000    0.050000
    7:    0.900000    0.100000
    8:    1.000000    1.000000
  Using polynomial approximant of degree 2

  L2 data approximation error = 0.14598

  Normalized length of piecewise linear interpolant = 3.25908
  Normalized length of polynomial approximant       = 1.03194
  Created plot file "p04_poly02.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #4.
  Number of data points = 8

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    0.050000    0.700000
    3:    0.100000    1.000000
    4:    0.200000    1.000000
    5:    0.800000    0.300000
    6:    0.850000    0.050000
    7:    0.900000    0.100000
    8:    1.000000    1.000000
  Using polynomial approximant of degree 3

  L2 data approximation error = 0.0559589

  Normalized length of piecewise linear interpolant = 3.25908
  Normalized length of polynomial approximant       = 3.3304
  Created plot file "p04_poly03.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #4.
  Number of data points = 8

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    0.050000    0.700000
    3:    0.100000    1.000000
    4:    0.200000    1.000000
    5:    0.800000    0.300000
    6:    0.850000    0.050000
    7:    0.900000    0.100000
    8:    1.000000    1.000000
  Using polynomial approximant of degree 4

  L2 data approximation error = 0.0559577

  Normalized length of piecewise linear interpolant = 3.25908
  Normalized length of polynomial approximant       = 3.32957
  Created plot file "p04_poly04.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #4.
  Number of data points = 8

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    0.050000    0.700000
    3:    0.100000    1.000000
    4:    0.200000    1.000000
    5:    0.800000    0.300000
    6:    0.850000    0.050000
    7:    0.900000    0.100000
    8:    1.000000    1.000000
  Using polynomial approximant of degree 5

  L2 data approximation error = 0.00829484

  Normalized length of piecewise linear interpolant = 3.25908
  Normalized length of polynomial approximant       = 3.58478
  Created plot file "p04_poly05.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #4.
  Number of data points = 8

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    0.050000    0.700000
    3:    0.100000    1.000000
    4:    0.200000    1.000000
    5:    0.800000    0.300000
    6:    0.850000    0.050000
    7:    0.900000    0.100000
    8:    1.000000    1.000000
  Using polynomial approximant of degree 9

  L2 data approximation error = 9.36892e-15

  Normalized length of piecewise linear interpolant = 3.25908
  Normalized length of polynomial approximant       = 4.81669
  Created plot file "p04_poly09.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #4.
  Number of data points = 8

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    0.050000    0.700000
    3:    0.100000    1.000000
    4:    0.200000    1.000000
    5:    0.800000    0.300000
    6:    0.850000    0.050000
    7:    0.900000    0.100000
    8:    1.000000    1.000000
  Using polynomial approximant of degree 12

  L2 data approximation error = 2.24558e-14

  Normalized length of piecewise linear interpolant = 3.25908
  Normalized length of polynomial approximant       = 4.89584
  Created plot file "p04_poly12.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #5.
  Number of data points = 9

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    0.100000    0.900000
    3:    0.200000    0.950000
    4:    0.300000    0.900000
    5:    0.400000    0.100000
    6:    0.500000    0.050000
    7:    0.600000    0.050000
    8:    0.800000    0.200000
    9:    1.000000    1.000000
  Using polynomial approximant of degree 0

  L2 data approximation error = 0.143324

  Normalized length of piecewise linear interpolant = 3.2218
  Normalized length of polynomial approximant       = 1
  Created plot file "p05_poly00.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #5.
  Number of data points = 9

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    0.100000    0.900000
    3:    0.200000    0.950000
    4:    0.300000    0.900000
    5:    0.400000    0.100000
    6:    0.500000    0.050000
    7:    0.600000    0.050000
    8:    0.800000    0.200000
    9:    1.000000    1.000000
  Using polynomial approximant of degree 1

  L2 data approximation error = 0.143322

  Normalized length of piecewise linear interpolant = 3.2218
  Normalized length of polynomial approximant       = 1.00003

  Created plot file "p05_data.png".
  Created plot file "p05_poly01.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #5.
  Number of data points = 9

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    0.100000    0.900000
    3:    0.200000    0.950000
    4:    0.300000    0.900000
    5:    0.400000    0.100000
    6:    0.500000    0.050000
    7:    0.600000    0.050000
    8:    0.800000    0.200000
    9:    1.000000    1.000000
  Using polynomial approximant of degree 2

  L2 data approximation error = 0.13517

  Normalized length of piecewise linear interpolant = 3.2218
  Normalized length of polynomial approximant       = 1.31038
  Created plot file "p05_poly02.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #5.
  Number of data points = 9

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    0.100000    0.900000
    3:    0.200000    0.950000
    4:    0.300000    0.900000
    5:    0.400000    0.100000
    6:    0.500000    0.050000
    7:    0.600000    0.050000
    8:    0.800000    0.200000
    9:    1.000000    1.000000
  Using polynomial approximant of degree 3

  L2 data approximation error = 0.0717904

  Normalized length of piecewise linear interpolant = 3.2218
  Normalized length of polynomial approximant       = 3.05546
  Created plot file "p05_poly03.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #5.
  Number of data points = 9

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    0.100000    0.900000
    3:    0.200000    0.950000
    4:    0.300000    0.900000
    5:    0.400000    0.100000
    6:    0.500000    0.050000
    7:    0.600000    0.050000
    8:    0.800000    0.200000
    9:    1.000000    1.000000
  Using polynomial approximant of degree 4

  L2 data approximation error = 0.0391096

  Normalized length of piecewise linear interpolant = 3.2218
  Normalized length of polynomial approximant       = 3.42544
  Created plot file "p05_poly04.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #5.
  Number of data points = 9

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    0.100000    0.900000
    3:    0.200000    0.950000
    4:    0.300000    0.900000
    5:    0.400000    0.100000
    6:    0.500000    0.050000
    7:    0.600000    0.050000
    8:    0.800000    0.200000
    9:    1.000000    1.000000
  Using polynomial approximant of degree 5

  L2 data approximation error = 0.03589

  Normalized length of piecewise linear interpolant = 3.2218
  Normalized length of polynomial approximant       = 3.41454
  Created plot file "p05_poly05.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #5.
  Number of data points = 9

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    0.100000    0.900000
    3:    0.200000    0.950000
    4:    0.300000    0.900000
    5:    0.400000    0.100000
    6:    0.500000    0.050000
    7:    0.600000    0.050000
    8:    0.800000    0.200000
    9:    1.000000    1.000000
  Using polynomial approximant of degree 9

  L2 data approximation error = 3.02496e-12

  Normalized length of piecewise linear interpolant = 3.2218
  Normalized length of polynomial approximant       = 47.9536
  Created plot file "p05_poly09.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #5.
  Number of data points = 9

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    0.000000
    2:    0.100000    0.900000
    3:    0.200000    0.950000
    4:    0.300000    0.900000
    5:    0.400000    0.100000
    6:    0.500000    0.050000
    7:    0.600000    0.050000
    8:    0.800000    0.200000
    9:    1.000000    1.000000
  Using polynomial approximant of degree 12

  L2 data approximation error = 9.77135e-13

  Normalized length of piecewise linear interpolant = 3.2218
  Normalized length of polynomial approximant       = 125.388
  Created plot file "p05_poly12.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #6.
  Number of data points = 49

  Data array:

  Row:       1             2       
  Col
    1:  595.000000    0.644000
    2:  605.000000    0.622000
    3:  615.000000    0.638000
    4:  625.000000    0.649000
    5:  635.000000    0.652000
    6:  645.000000    0.639000
    7:  655.000000    0.646000
    8:  665.000000    0.657000
    9:  675.000000    0.652000
   10:  685.000000    0.655000
   11:  695.000000    0.644000
   12:  705.000000    0.663000
   13:  715.000000    0.663000
   14:  725.000000    0.668000
   15:  735.000000    0.676000
   16:  745.000000    0.676000
   17:  755.000000    0.686000
   18:  765.000000    0.679000
   19:  775.000000    0.678000
   20:  785.000000    0.683000
   21:  795.000000    0.694000
   22:  805.000000    0.699000
   23:  815.000000    0.710000
   24:  825.000000    0.730000
   25:  835.000000    0.763000
   26:  845.000000    0.812000
   27:  855.000000    0.907000
   28:  865.000000    1.044000
   29:  875.000000    1.336000
   30:  885.000000    1.881000
   31:  895.000000    2.169000
   32:  905.000000    2.075000
   33:  915.000000    1.598000
   34:  925.000000    1.211000
   35:  935.000000    0.916000
   36:  945.000000    0.746000
   37:  955.000000    0.672000
   38:  965.000000    0.627000
   39:  975.000000    0.615000
   40:  985.000000    0.607000
   41:  995.000000    0.606000
   42: 1005.000000    0.609000
   43: 1015.000000    0.603000
   44: 1025.000000    0.601000
   45: 1035.000000    0.603000
   46: 1045.000000    0.601000
   47: 1055.000000    0.611000
   48: 1065.000000    0.601000
   49: 1075.000000    0.608000
  Using polynomial approximant of degree 0

  L2 data approximation error = 0.0530251

  Normalized length of piecewise linear interpolant = 2.68209
  Normalized length of polynomial approximant       = 1
  Created plot file "p06_poly00.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #6.
  Number of data points = 49

  Data array:

  Row:       1             2       
  Col
    1:  595.000000    0.644000
    2:  605.000000    0.622000
    3:  615.000000    0.638000
    4:  625.000000    0.649000
    5:  635.000000    0.652000
    6:  645.000000    0.639000
    7:  655.000000    0.646000
    8:  665.000000    0.657000
    9:  675.000000    0.652000
   10:  685.000000    0.655000
   11:  695.000000    0.644000
   12:  705.000000    0.663000
   13:  715.000000    0.663000
   14:  725.000000    0.668000
   15:  735.000000    0.676000
   16:  745.000000    0.676000
   17:  755.000000    0.686000
   18:  765.000000    0.679000
   19:  775.000000    0.678000
   20:  785.000000    0.683000
   21:  795.000000    0.694000
   22:  805.000000    0.699000
   23:  815.000000    0.710000
   24:  825.000000    0.730000
   25:  835.000000    0.763000
   26:  845.000000    0.812000
   27:  855.000000    0.907000
   28:  865.000000    1.044000
   29:  875.000000    1.336000
   30:  885.000000    1.881000
   31:  895.000000    2.169000
   32:  905.000000    2.075000
   33:  915.000000    1.598000
   34:  925.000000    1.211000
   35:  935.000000    0.916000
   36:  945.000000    0.746000
   37:  955.000000    0.672000
   38:  965.000000    0.627000
   39:  975.000000    0.615000
   40:  985.000000    0.607000
   41:  995.000000    0.606000
   42: 1005.000000    0.609000
   43: 1015.000000    0.603000
   44: 1025.000000    0.601000
   45: 1035.000000    0.603000
   46: 1045.000000    0.601000
   47: 1055.000000    0.611000
   48: 1065.000000    0.601000
   49: 1075.000000    0.608000
  Using polynomial approximant of degree 1

  L2 data approximation error = 0.0525121

  Normalized length of piecewise linear interpolant = 2.68209
  Normalized length of polynomial approximant       = 1.0062

  Created plot file "p06_data.png".
  Created plot file "p06_poly01.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #6.
  Number of data points = 49

  Data array:

  Row:       1             2       
  Col
    1:  595.000000    0.644000
    2:  605.000000    0.622000
    3:  615.000000    0.638000
    4:  625.000000    0.649000
    5:  635.000000    0.652000
    6:  645.000000    0.639000
    7:  655.000000    0.646000
    8:  665.000000    0.657000
    9:  675.000000    0.652000
   10:  685.000000    0.655000
   11:  695.000000    0.644000
   12:  705.000000    0.663000
   13:  715.000000    0.663000
   14:  725.000000    0.668000
   15:  735.000000    0.676000
   16:  745.000000    0.676000
   17:  755.000000    0.686000
   18:  765.000000    0.679000
   19:  775.000000    0.678000
   20:  785.000000    0.683000
   21:  795.000000    0.694000
   22:  805.000000    0.699000
   23:  815.000000    0.710000
   24:  825.000000    0.730000
   25:  835.000000    0.763000
   26:  845.000000    0.812000
   27:  855.000000    0.907000
   28:  865.000000    1.044000
   29:  875.000000    1.336000
   30:  885.000000    1.881000
   31:  895.000000    2.169000
   32:  905.000000    2.075000
   33:  915.000000    1.598000
   34:  925.000000    1.211000
   35:  935.000000    0.916000
   36:  945.000000    0.746000
   37:  955.000000    0.672000
   38:  965.000000    0.627000
   39:  975.000000    0.615000
   40:  985.000000    0.607000
   41:  995.000000    0.606000
   42: 1005.000000    0.609000
   43: 1015.000000    0.603000
   44: 1025.000000    0.601000
   45: 1035.000000    0.603000
   46: 1045.000000    0.601000
   47: 1055.000000    0.611000
   48: 1065.000000    0.601000
   49: 1075.000000    0.608000
  Using polynomial approximant of degree 2

  L2 data approximation error = 0.0473605

  Normalized length of piecewise linear interpolant = 2.68209
  Normalized length of polynomial approximant       = 1.2402
  Created plot file "p06_poly02.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #6.
  Number of data points = 49

  Data array:

  Row:       1             2       
  Col
    1:  595.000000    0.644000
    2:  605.000000    0.622000
    3:  615.000000    0.638000
    4:  625.000000    0.649000
    5:  635.000000    0.652000
    6:  645.000000    0.639000
    7:  655.000000    0.646000
    8:  665.000000    0.657000
    9:  675.000000    0.652000
   10:  685.000000    0.655000
   11:  695.000000    0.644000
   12:  705.000000    0.663000
   13:  715.000000    0.663000
   14:  725.000000    0.668000
   15:  735.000000    0.676000
   16:  745.000000    0.676000
   17:  755.000000    0.686000
   18:  765.000000    0.679000
   19:  775.000000    0.678000
   20:  785.000000    0.683000
   21:  795.000000    0.694000
   22:  805.000000    0.699000
   23:  815.000000    0.710000
   24:  825.000000    0.730000
   25:  835.000000    0.763000
   26:  845.000000    0.812000
   27:  855.000000    0.907000
   28:  865.000000    1.044000
   29:  875.000000    1.336000
   30:  885.000000    1.881000
   31:  895.000000    2.169000
   32:  905.000000    2.075000
   33:  915.000000    1.598000
   34:  925.000000    1.211000
   35:  935.000000    0.916000
   36:  945.000000    0.746000
   37:  955.000000    0.672000
   38:  965.000000    0.627000
   39:  975.000000    0.615000
   40:  985.000000    0.607000
   41:  995.000000    0.606000
   42: 1005.000000    0.609000
   43: 1015.000000    0.603000
   44: 1025.000000    0.601000
   45: 1035.000000    0.603000
   46: 1045.000000    0.601000
   47: 1055.000000    0.611000
   48: 1065.000000    0.601000
   49: 1075.000000    0.608000
  Using polynomial approximant of degree 3

  L2 data approximation error = 0.0437687

  Normalized length of piecewise linear interpolant = 2.68209
  Normalized length of polynomial approximant       = 1.43902
  Created plot file "p06_poly03.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #6.
  Number of data points = 49

  Data array:

  Row:       1             2       
  Col
    1:  595.000000    0.644000
    2:  605.000000    0.622000
    3:  615.000000    0.638000
    4:  625.000000    0.649000
    5:  635.000000    0.652000
    6:  645.000000    0.639000
    7:  655.000000    0.646000
    8:  665.000000    0.657000
    9:  675.000000    0.652000
   10:  685.000000    0.655000
   11:  695.000000    0.644000
   12:  705.000000    0.663000
   13:  715.000000    0.663000
   14:  725.000000    0.668000
   15:  735.000000    0.676000
   16:  745.000000    0.676000
   17:  755.000000    0.686000
   18:  765.000000    0.679000
   19:  775.000000    0.678000
   20:  785.000000    0.683000
   21:  795.000000    0.694000
   22:  805.000000    0.699000
   23:  815.000000    0.710000
   24:  825.000000    0.730000
   25:  835.000000    0.763000
   26:  845.000000    0.812000
   27:  855.000000    0.907000
   28:  865.000000    1.044000
   29:  875.000000    1.336000
   30:  885.000000    1.881000
   31:  895.000000    2.169000
   32:  905.000000    2.075000
   33:  915.000000    1.598000
   34:  925.000000    1.211000
   35:  935.000000    0.916000
   36:  945.000000    0.746000
   37:  955.000000    0.672000
   38:  965.000000    0.627000
   39:  975.000000    0.615000
   40:  985.000000    0.607000
   41:  995.000000    0.606000
   42: 1005.000000    0.609000
   43: 1015.000000    0.603000
   44: 1025.000000    0.601000
   45: 1035.000000    0.603000
   46: 1045.000000    0.601000
   47: 1055.000000    0.611000
   48: 1065.000000    0.601000
   49: 1075.000000    0.608000
  Using polynomial approximant of degree 4
[Warning: Rank deficient, rank = 4, tol =  5.115918e-02.] 
[> In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('vandermonde_approx_1d_test01', '/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test01.m', 47)" style="font-weight:bold">vandermonde_approx_1d_test01</a> (<a href="matlab: opentoline('/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test01.m',47,0)">line 47</a>)
  In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('vandermonde_approx_1d_test', '/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test.m', 32)" style="font-weight:bold">vandermonde_approx_1d_test</a> (<a href="matlab: opentoline('/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test.m',32,0)">line 32</a>)
] 

  L2 data approximation error = 0.0443293

  Normalized length of piecewise linear interpolant = 2.68209
  Normalized length of polynomial approximant       = 1.41035
  Created plot file "p06_poly04.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #6.
  Number of data points = 49

  Data array:

  Row:       1             2       
  Col
    1:  595.000000    0.644000
    2:  605.000000    0.622000
    3:  615.000000    0.638000
    4:  625.000000    0.649000
    5:  635.000000    0.652000
    6:  645.000000    0.639000
    7:  655.000000    0.646000
    8:  665.000000    0.657000
    9:  675.000000    0.652000
   10:  685.000000    0.655000
   11:  695.000000    0.644000
   12:  705.000000    0.663000
   13:  715.000000    0.663000
   14:  725.000000    0.668000
   15:  735.000000    0.676000
   16:  745.000000    0.676000
   17:  755.000000    0.686000
   18:  765.000000    0.679000
   19:  775.000000    0.678000
   20:  785.000000    0.683000
   21:  795.000000    0.694000
   22:  805.000000    0.699000
   23:  815.000000    0.710000
   24:  825.000000    0.730000
   25:  835.000000    0.763000
   26:  845.000000    0.812000
   27:  855.000000    0.907000
   28:  865.000000    1.044000
   29:  875.000000    1.336000
   30:  885.000000    1.881000
   31:  895.000000    2.169000
   32:  905.000000    2.075000
   33:  915.000000    1.598000
   34:  925.000000    1.211000
   35:  935.000000    0.916000
   36:  945.000000    0.746000
   37:  955.000000    0.672000
   38:  965.000000    0.627000
   39:  975.000000    0.615000
   40:  985.000000    0.607000
   41:  995.000000    0.606000
   42: 1005.000000    0.609000
   43: 1015.000000    0.603000
   44: 1025.000000    0.601000
   45: 1035.000000    0.603000
   46: 1045.000000    0.601000
   47: 1055.000000    0.611000
   48: 1065.000000    0.601000
   49: 1075.000000    0.608000
  Using polynomial approximant of degree 5
[Warning: Rank deficient, rank = 4, tol =  5.005005e+01.] 
[> In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('vandermonde_approx_1d_test01', '/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test01.m', 47)" style="font-weight:bold">vandermonde_approx_1d_test01</a> (<a href="matlab: opentoline('/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test01.m',47,0)">line 47</a>)
  In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('vandermonde_approx_1d_test', '/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test.m', 32)" style="font-weight:bold">vandermonde_approx_1d_test</a> (<a href="matlab: opentoline('/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test.m',32,0)">line 32</a>)
] 

  L2 data approximation error = 0.0448312

  Normalized length of piecewise linear interpolant = 2.68209
  Normalized length of polynomial approximant       = 1.39049
  Created plot file "p06_poly05.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #6.
  Number of data points = 49

  Data array:

  Row:       1             2       
  Col
    1:  595.000000    0.644000
    2:  605.000000    0.622000
    3:  615.000000    0.638000
    4:  625.000000    0.649000
    5:  635.000000    0.652000
    6:  645.000000    0.639000
    7:  655.000000    0.646000
    8:  665.000000    0.657000
    9:  675.000000    0.652000
   10:  685.000000    0.655000
   11:  695.000000    0.644000
   12:  705.000000    0.663000
   13:  715.000000    0.663000
   14:  725.000000    0.668000
   15:  735.000000    0.676000
   16:  745.000000    0.676000
   17:  755.000000    0.686000
   18:  765.000000    0.679000
   19:  775.000000    0.678000
   20:  785.000000    0.683000
   21:  795.000000    0.694000
   22:  805.000000    0.699000
   23:  815.000000    0.710000
   24:  825.000000    0.730000
   25:  835.000000    0.763000
   26:  845.000000    0.812000
   27:  855.000000    0.907000
   28:  865.000000    1.044000
   29:  875.000000    1.336000
   30:  885.000000    1.881000
   31:  895.000000    2.169000
   32:  905.000000    2.075000
   33:  915.000000    1.598000
   34:  925.000000    1.211000
   35:  935.000000    0.916000
   36:  945.000000    0.746000
   37:  955.000000    0.672000
   38:  965.000000    0.627000
   39:  975.000000    0.615000
   40:  985.000000    0.607000
   41:  995.000000    0.606000
   42: 1005.000000    0.609000
   43: 1015.000000    0.603000
   44: 1025.000000    0.601000
   45: 1035.000000    0.603000
   46: 1045.000000    0.601000
   47: 1055.000000    0.611000
   48: 1065.000000    0.601000
   49: 1075.000000    0.608000
  Using polynomial approximant of degree 9
[Warning: Rank deficient, rank = 4, tol =  5.182242e+13.] 
[> In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('vandermonde_approx_1d_test01', '/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test01.m', 47)" style="font-weight:bold">vandermonde_approx_1d_test01</a> (<a href="matlab: opentoline('/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test01.m',47,0)">line 47</a>)
  In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('vandermonde_approx_1d_test', '/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test.m', 32)" style="font-weight:bold">vandermonde_approx_1d_test</a> (<a href="matlab: opentoline('/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test.m',32,0)">line 32</a>)
] 

  L2 data approximation error = 0.0447827

  Normalized length of piecewise linear interpolant = 2.68209
  Normalized length of polynomial approximant       = 1.35233
  Created plot file "p06_poly09.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #6.
  Number of data points = 49

  Data array:

  Row:       1             2       
  Col
    1:  595.000000    0.644000
    2:  605.000000    0.622000
    3:  615.000000    0.638000
    4:  625.000000    0.649000
    5:  635.000000    0.652000
    6:  645.000000    0.639000
    7:  655.000000    0.646000
    8:  665.000000    0.657000
    9:  675.000000    0.652000
   10:  685.000000    0.655000
   11:  695.000000    0.644000
   12:  705.000000    0.663000
   13:  715.000000    0.663000
   14:  725.000000    0.668000
   15:  735.000000    0.676000
   16:  745.000000    0.676000
   17:  755.000000    0.686000
   18:  765.000000    0.679000
   19:  775.000000    0.678000
   20:  785.000000    0.683000
   21:  795.000000    0.694000
   22:  805.000000    0.699000
   23:  815.000000    0.710000
   24:  825.000000    0.730000
   25:  835.000000    0.763000
   26:  845.000000    0.812000
   27:  855.000000    0.907000
   28:  865.000000    1.044000
   29:  875.000000    1.336000
   30:  885.000000    1.881000
   31:  895.000000    2.169000
   32:  905.000000    2.075000
   33:  915.000000    1.598000
   34:  925.000000    1.211000
   35:  935.000000    0.916000
   36:  945.000000    0.746000
   37:  955.000000    0.672000
   38:  965.000000    0.627000
   39:  975.000000    0.615000
   40:  985.000000    0.607000
   41:  995.000000    0.606000
   42: 1005.000000    0.609000
   43: 1015.000000    0.603000
   44: 1025.000000    0.601000
   45: 1035.000000    0.603000
   46: 1045.000000    0.601000
   47: 1055.000000    0.611000
   48: 1065.000000    0.601000
   49: 1075.000000    0.608000
  Using polynomial approximant of degree 12
[Warning: Rank deficient, rank = 4, tol =  5.688501e+22.] 
[> In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('vandermonde_approx_1d_test01', '/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test01.m', 47)" style="font-weight:bold">vandermonde_approx_1d_test01</a> (<a href="matlab: opentoline('/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test01.m',47,0)">line 47</a>)
  In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('vandermonde_approx_1d_test', '/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test.m', 32)" style="font-weight:bold">vandermonde_approx_1d_test</a> (<a href="matlab: opentoline('/home/burkardt/public_html/m_src/vandermonde_approx_1d_test/vandermonde_approx_1d_test.m',32,0)">line 32</a>)
] 

  L2 data approximation error = 0.0449233

  Normalized length of piecewise linear interpolant = 2.68209
  Normalized length of polynomial approximant       = 1.52582
  Created plot file "p06_poly12.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #7.
  Number of data points = 4

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    1.000000
    2:    1.000000    2.000000
    3:    4.000000    2.000000
    4:    5.000000    1.000000
  Using polynomial approximant of degree 0

  L2 data approximation error = 0.25

  Normalized length of piecewise linear interpolant = 2.63961
  Normalized length of polynomial approximant       = 1
  Created plot file "p07_poly00.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #7.
  Number of data points = 4

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    1.000000
    2:    1.000000    2.000000
    3:    4.000000    2.000000
    4:    5.000000    1.000000
  Using polynomial approximant of degree 1

  L2 data approximation error = 0.25

  Normalized length of piecewise linear interpolant = 2.63961
  Normalized length of polynomial approximant       = 1

  Created plot file "p07_data.png".
  Created plot file "p07_poly01.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #7.
  Number of data points = 4

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    1.000000
    2:    1.000000    2.000000
    3:    4.000000    2.000000
    4:    5.000000    1.000000
  Using polynomial approximant of degree 2

  L2 data approximation error = 8.00593e-16

  Normalized length of piecewise linear interpolant = 2.63961
  Normalized length of polynomial approximant       = 3.36731
  Created plot file "p07_poly02.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #7.
  Number of data points = 4

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    1.000000
    2:    1.000000    2.000000
    3:    4.000000    2.000000
    4:    5.000000    1.000000
  Using polynomial approximant of degree 3

  L2 data approximation error = 2.77556e-16

  Normalized length of piecewise linear interpolant = 2.63961
  Normalized length of polynomial approximant       = 3.36731
  Created plot file "p07_poly03.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #7.
  Number of data points = 4

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    1.000000
    2:    1.000000    2.000000
    3:    4.000000    2.000000
    4:    5.000000    1.000000
  Using polynomial approximant of degree 4

  L2 data approximation error = 3.59753e-16

  Normalized length of piecewise linear interpolant = 2.63961
  Normalized length of polynomial approximant       = 3.58258
  Created plot file "p07_poly04.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #7.
  Number of data points = 4

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    1.000000
    2:    1.000000    2.000000
    3:    4.000000    2.000000
    4:    5.000000    1.000000
  Using polynomial approximant of degree 5

  L2 data approximation error = 5.02675e-16

  Normalized length of piecewise linear interpolant = 2.63961
  Normalized length of polynomial approximant       = 3.90825
  Created plot file "p07_poly05.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #7.
  Number of data points = 4

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    1.000000
    2:    1.000000    2.000000
    3:    4.000000    2.000000
    4:    5.000000    1.000000
  Using polynomial approximant of degree 9

  L2 data approximation error = 4.2119e-15

  Normalized length of piecewise linear interpolant = 2.63961
  Normalized length of polynomial approximant       = 6.52763
  Created plot file "p07_poly09.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #7.
  Number of data points = 4

  Data array:

  Row:       1             2       
  Col
    1:    0.000000    1.000000
    2:    1.000000    2.000000
    3:    4.000000    2.000000
    4:    5.000000    1.000000
  Using polynomial approximant of degree 12

  L2 data approximation error = 2.44816e-15

  Normalized length of piecewise linear interpolant = 2.63961
  Normalized length of polynomial approximant       = 10.4248
  Created plot file "p07_poly12.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #8.
  Number of data points = 12

  Data array:

  Row:       1             2       
  Col
    1:   -1.000000    1.000000
    2:   -0.800000    0.640000
    3:   -0.600000    0.360000
    4:   -0.400000    0.160000
    5:   -0.200000    0.040000
    6:    0.000000    0.000000
    7:    0.200000    0.040000
    8:    0.200010    0.050000
    9:    0.400000    0.160000
   10:    0.600000    0.360000
   11:    0.800000    0.640000
   12:    1.000000    1.000000
  Using polynomial approximant of degree 0

  L2 data approximation error = 0.101554

  Normalized length of piecewise linear interpolant = 2.31939
  Normalized length of polynomial approximant       = 1
  Created plot file "p08_poly00.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #8.
  Number of data points = 12

  Data array:

  Row:       1             2       
  Col
    1:   -1.000000    1.000000
    2:   -0.800000    0.640000
    3:   -0.600000    0.360000
    4:   -0.400000    0.160000
    5:   -0.200000    0.040000
    6:    0.000000    0.000000
    7:    0.200000    0.040000
    8:    0.200010    0.050000
    9:    0.400000    0.160000
   10:    0.600000    0.360000
   11:    0.800000    0.640000
   12:    1.000000    1.000000
  Using polynomial approximant of degree 1

  L2 data approximation error = 0.101522

  Normalized length of piecewise linear interpolant = 2.31939
  Normalized length of polynomial approximant       = 1.00042

  Created plot file "p08_data.png".
  Created plot file "p08_poly01.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #8.
  Number of data points = 12

  Data array:

  Row:       1             2       
  Col
    1:   -1.000000    1.000000
    2:   -0.800000    0.640000
    3:   -0.600000    0.360000
    4:   -0.400000    0.160000
    5:   -0.200000    0.040000
    6:    0.000000    0.000000
    7:    0.200000    0.040000
    8:    0.200010    0.050000
    9:    0.400000    0.160000
   10:    0.600000    0.360000
   11:    0.800000    0.640000
   12:    1.000000    1.000000
  Using polynomial approximant of degree 2

  L2 data approximation error = 0.000762201

  Normalized length of piecewise linear interpolant = 2.31939
  Normalized length of polynomial approximant       = 2.31944
  Created plot file "p08_poly02.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #8.
  Number of data points = 12

  Data array:

  Row:       1             2       
  Col
    1:   -1.000000    1.000000
    2:   -0.800000    0.640000
    3:   -0.600000    0.360000
    4:   -0.400000    0.160000
    5:   -0.200000    0.040000
    6:    0.000000    0.000000
    7:    0.200000    0.040000
    8:    0.200010    0.050000
    9:    0.400000    0.160000
   10:    0.600000    0.360000
   11:    0.800000    0.640000
   12:    1.000000    1.000000
  Using polynomial approximant of degree 3

  L2 data approximation error = 0.000748027

  Normalized length of piecewise linear interpolant = 2.31939
  Normalized length of polynomial approximant       = 2.31959
  Created plot file "p08_poly03.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #8.
  Number of data points = 12

  Data array:

  Row:       1             2       
  Col
    1:   -1.000000    1.000000
    2:   -0.800000    0.640000
    3:   -0.600000    0.360000
    4:   -0.400000    0.160000
    5:   -0.200000    0.040000
    6:    0.000000    0.000000
    7:    0.200000    0.040000
    8:    0.200010    0.050000
    9:    0.400000    0.160000
   10:    0.600000    0.360000
   11:    0.800000    0.640000
   12:    1.000000    1.000000
  Using polynomial approximant of degree 4

  L2 data approximation error = 0.000731706

  Normalized length of piecewise linear interpolant = 2.31939
  Normalized length of polynomial approximant       = 2.32028
  Created plot file "p08_poly04.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #8.
  Number of data points = 12

  Data array:

  Row:       1             2       
  Col
    1:   -1.000000    1.000000
    2:   -0.800000    0.640000
    3:   -0.600000    0.360000
    4:   -0.400000    0.160000
    5:   -0.200000    0.040000
    6:    0.000000    0.000000
    7:    0.200000    0.040000
    8:    0.200010    0.050000
    9:    0.400000    0.160000
   10:    0.600000    0.360000
   11:    0.800000    0.640000
   12:    1.000000    1.000000
  Using polynomial approximant of degree 5

  L2 data approximation error = 0.000704364

  Normalized length of piecewise linear interpolant = 2.31939
  Normalized length of polynomial approximant       = 2.32052
  Created plot file "p08_poly05.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #8.
  Number of data points = 12

  Data array:

  Row:       1             2       
  Col
    1:   -1.000000    1.000000
    2:   -0.800000    0.640000
    3:   -0.600000    0.360000
    4:   -0.400000    0.160000
    5:   -0.200000    0.040000
    6:    0.000000    0.000000
    7:    0.200000    0.040000
    8:    0.200010    0.050000
    9:    0.400000    0.160000
   10:    0.600000    0.360000
   11:    0.800000    0.640000
   12:    1.000000    1.000000
  Using polynomial approximant of degree 9

  L2 data approximation error = 0.000627667

  Normalized length of piecewise linear interpolant = 2.31939
  Normalized length of polynomial approximant       = 2.32096
  Created plot file "p08_poly09.png".

VANDERMONDE_APPROX_1D_TEST01:
  Approximate data from TEST_INTERP problem #8.
  Number of data points = 12

  Data array:

  Row:       1             2       
  Col
    1:   -1.000000    1.000000
    2:   -0.800000    0.640000
    3:   -0.600000    0.360000
    4:   -0.400000    0.160000
    5:   -0.200000    0.040000
    6:    0.000000    0.000000
    7:    0.200000    0.040000
    8:    0.200010    0.050000
    9:    0.400000    0.160000
   10:    0.600000    0.360000
   11:    0.800000    0.640000
   12:    1.000000    1.000000
  Using polynomial approximant of degree 12

  L2 data approximation error = 4.23538e-11

  Normalized length of piecewise linear interpolant = 2.31939
  Normalized length of polynomial approximant       = 23167
  Created plot file "p08_poly12.png".

vandermonde_approx_1d_test:
  Normal end of execution.

18-Feb-2019 20:36:18