02 March 2008 05:00:24 PM

INT_EXACTNESS_CHEBYSHEV1
  C++ version

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

INT_EXACTNESS_CHEBYSHEV1: User input:
  Quadrature rule X file = "cheby1_o16_x.txt".
  Quadrature rule W file = "cheby1_o16_w.txt".
  Quadrature rule R file = "cheby1_o16_r.txt".
  Maximum degree to check = 35

  Spatial dimension = 1
  Number of points  = 16

  The quadrature rule to be tested is
  a Gauss-Legendre rule
  ORDER = 16

  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] =       0.1963495408493621
  w[ 1] =       0.1963495408493621
  w[ 2] =       0.1963495408493621
  w[ 3] =       0.1963495408493621
  w[ 4] =       0.1963495408493621
  w[ 5] =       0.1963495408493621
  w[ 6] =       0.1963495408493621
  w[ 7] =       0.1963495408493621
  w[ 8] =       0.1963495408493621
  w[ 9] =       0.1963495408493621
  w[10] =       0.1963495408493621
  w[11] =       0.1963495408493621
  w[12] =       0.1963495408493621
  w[13] =       0.1963495408493621
  w[14] =       0.1963495408493621
  w[15] =       0.1963495408493621

  Abscissas X:

  x[ 0] =      -0.9951847266721968
  x[ 1] =      -0.9569403357322088
  x[ 2] =      -0.8819212643483549
  x[ 3] =       -0.773010453362737
  x[ 4] =      -0.6343932841636454
  x[ 5] =      -0.4713967368259977
  x[ 6] =      -0.2902846772544622
  x[ 7] =     -0.09801714032956065
  x[ 8] =      0.09801714032956076
  x[ 9] =       0.2902846772544623
  x[10] =       0.4713967368259978
  x[11] =       0.6343932841636455
  x[12] =        0.773010453362737
  x[13] =        0.881921264348355
  x[14] =       0.9569403357322088
  x[15] =       0.9951847266721968

  Region R:

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

  A Gauss-Chebyshev type 1 rule would be able to exactly
  integrate monomials up to and including degree = 31

          Error          Degree

     4.240739575284689e-16   0
     8.326672684688674e-17   1
                         0   2
     8.326672684688674e-17   3
                         0   4
     2.775557561562891e-17   5
     2.261727773485168e-16   6
     1.387778780781446e-16   7
     1.292415870562953e-16   8
     2.775557561562891e-17   9
     1.436017633958837e-16  10
     1.110223024625157e-16  11
     1.566564691591458e-16  12
                         0  13
     3.374139335735448e-16  14
     5.551115123125783e-17  15
     3.599081958117811e-16  16
     5.551115123125783e-17  17
     7.621585323073012e-16  18
                         0  19
     8.022721392708434e-16  20
     2.775557561562891e-17  21
     6.303566808556627e-16  22
                         0  23
     1.315526986133557e-15  24
     2.775557561562891e-17  25
     9.120987103859327e-16  26
     2.775557561562891e-17  27
     1.064115162116922e-15  28
                         0  29
     1.223120875996462e-15  30
                         0  31
       3.3273433102101e-09  32
                         0  33
     2.913945057385399e-08  34
     2.775557561562891e-17  35

INT_EXACTNESS_CHEBYSHEV1:
  Normal end of execution.

02 March 2008 05:00:24 PM