20 January 2020 09:15:51 AM

HERMITE_EXACTNESS
  C version

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

  The quadrature file rootname is "hermite_probabilist_010".

  The requested maximum monomial degree is = 5

HERMITE_EXACTNESS: User input:
  Quadrature rule X file = "hermite_probabilist_010_x.txt".
  Quadrature rule W file = "hermite_probabilist_010_w.txt".
  Quadrature rule R file = "hermite_probabilist_010_r.txt".
  Maximum degree to check = 5

  Spatial dimension = 1
  Number of points  = 10

  The quadrature rule to be tested is
  a Gauss-Hermite rule
  ORDER = 10

  OPTION = 4, the probabilist normalized weighted rule for:
  Integral ( -oo < x < +oo ) f(x) * exp(-x*x/2) / sqrt(2 pi) dx

  Weights W:

  w[0] = 4.31065e-06
  w[1] = 0.000758071
  w[2] = 0.0191116
  w[3] = 0.135484
  w[4] = 0.344642
  w[5] = 0.344642
  w[6] = 0.135484
  w[7] = 0.0191116
  w[8] = 0.000758071
  w[9] = 4.31065e-06

  Abscissas X:

  x[0] = -4.85946
  x[1] = -3.58182
  x[2] = -2.48433
  x[3] = -1.46599
  x[4] = -0.484936
  x[5] = 0.484936
  x[6] = 1.46599
  x[7] = 2.48433
  x[8] = 3.58182
  x[9] = 4.85946

  Region R:

  r[0] = -1e+30
  r[1] = 1e+30

  A Gauss-Hermite rule would be able to exactly
  integrate monomials up to and including degree = 19

  Degree          Error

   0     2.220446049250313e-16
   1     4.977165598066269e-18
   2     2.220446049250313e-16
   3     6.396792817664476e-18
   4     1.480297366166875e-16
   5      1.07552855510562e-16

HERMITE_EXACTNESS:
  Normal end of execution.

20 January 2020 09:15:51 AM