03 March 2008 08:12:40 AM

INT_EXACTNESS_CHEBYSHEV2
  C++ version

  Investigate the polynomial exactness of a Gauss-Chebyshev
  type 2 quadrature rule by integrating weighted
  monomials up to a given degree over the [-1,+1] interval.

INT_EXACTNESS_CHEBYSHEV2: User input:
  Quadrature rule X file = "cheby2_o8_x.txt".
  Quadrature rule W file = "cheby2_o8_w.txt".
  Quadrature rule R file = "cheby2_o8_r.txt".
  Maximum degree to check = 18

  Spatial dimension = 1
  Number of points  = 8

  The quadrature rule to be tested is
  a Gauss-Legendre rule
  ORDER = 8

  Standard rule:
    Integral ( -1 <= x <= +1 ) f(x) dx
    is to be approximated by
    sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).

  Weights W:

  w[ 0] =      0.04083294770910712
  w[ 1] =       0.1442256007956728
  w[ 2] =       0.2617993877991495
  w[ 3] =        0.338540227093519
  w[ 4] =        0.338540227093519
  w[ 5] =       0.2617993877991494
  w[ 6] =       0.1442256007956728
  w[ 7] =      0.04083294770910708

  Abscissas X:

  x[ 0] =      -0.9396926207859084
  x[ 1] =      -0.7660444431189779
  x[ 2] =      -0.4999999999999998
  x[ 3] =      -0.1736481776669303
  x[ 4] =       0.1736481776669304
  x[ 5] =       0.5000000000000001
  x[ 6] =        0.766044443118978
  x[ 7] =       0.9396926207859084

  Region R:

  r[ 0] =                       -1
  r[ 1] =                        1

  A Gauss-Chebyshev type 2 rule would be able to exactly
  integrate monomials up to and including degree = 15

          Error          Degree

      1.41357985842823e-16   0
     3.469446951953614e-17   1
                         0   2
     8.326672684688674e-17   3
                         0   4
     2.775557561562891e-17   5
     1.130863886742584e-16   6
     3.469446951953614e-18   7
                         0   8
     3.469446951953614e-18   9
     2.154026450938255e-16  10
     3.469446951953614e-18  11
     2.741488210285052e-16  12
     3.469446951953614e-18  13
     5.061209003603172e-16  14
     3.469446951953614e-18  15
     0.0006993006992999631  16
     6.938893903907228e-18  17
      0.003290826820237859  18

INT_EXACTNESS_CHEBYSHEV2:
  Normal end of execution.

03 March 2008 08:12:40 AM