03 March 2008 08:12:35 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_o4_x.txt".
  Quadrature rule W file = "cheby2_o4_w.txt".
  Quadrature rule R file = "cheby2_o4_r.txt".
  Maximum degree to check = 10

  Spatial dimension = 1
  Number of points  = 4

  The quadrature rule to be tested is
  a Gauss-Legendre rule
  ORDER = 4

  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] =       0.2170787134227061
  w[ 1] =       0.5683194499747424
  w[ 2] =       0.5683194499747423
  w[ 3] =        0.217078713422706

  Abscissas X:

  x[ 0] =      -0.8090169943749473
  x[ 1] =      -0.3090169943749473
  x[ 2] =       0.3090169943749475
  x[ 3] =       0.8090169943749475

  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 = 7

          Error          Degree

      1.41357985842823e-16   0
     2.775557561562891e-17   1
                         0   2
     1.387778780781446e-17   3
      1.41357985842823e-16   4
     1.387778780781446e-17   5
     2.261727773485168e-16   6
     6.938893903907228e-18   7
       0.07142857142857151   8
     6.938893903907228e-18   9
        0.1904761904761903  10

INT_EXACTNESS_CHEBYSHEV2:
  Normal end of execution.

03 March 2008 08:12:35 AM