03 March 2008 09:12:42 AM

INT_EXACTNESS_GEGENBAUER
  C++ version

  Investigate the polynomial exactness of a Gauss-Gegenbauer
  quadrature rule by integrating exponentially weighted
  monomials up to a given degree over the (-oo,+oo) interval.

INT_EXACTNESS_GEGENBAUER: User input:
  Quadrature rule X file = "gegen_o4_a0.5_x.txt".
  Quadrature rule W file = "gegen_o4_a0.5_w.txt".
  Quadrature rule R file = "gegen_o4_a0.5_r.txt".
  Maximum degree to check = 10
  Exponent of (1-x^2), ALPHA = 0.5

  Spatial dimension = 1
  Number of points  = 4

  The quadrature rule to be tested is
  a Gauss-Gegenbauer rule
  ORDER = 4
  ALPHA = 0.5

  Standard rule:
    Integral ( -1 <= x <= +1 ) (1-x^2)^alpha f(x) dx
    is to be approximated by
    sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).

  Weights W:

  w[ 0] =        0.217078713422706
  w[ 1] =       0.5683194499747424
  w[ 2] =       0.5683194499747424
  w[ 3] =        0.217078713422706

  Abscissas X:

  x[ 0] =      -0.8090169943749475
  x[ 1] =      -0.3090169943749475
  x[ 2] =       0.3090169943749474
  x[ 3] =       0.8090169943749475

  Region R:

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

  A Gauss-Gegenbauer rule would be able to exactly
  integrate monomials up to and including degree = 7

          Error          Degree

     7.067899292141143e-16   0
     5.551115123125783e-17   1
     1.413579858428229e-16   2
                         0   3
     4.240739575284687e-16   4
                         0   5
     1.130863886742583e-16   6
                         0   7
       0.07142857142857166   8
                         0   9
        0.1904761904761884  10

INT_EXACTNESS_GEGENBAUER:
  Normal end of execution.

03 March 2008 09:12:42 AM