12 March 2020 04:11:01 PM
HERMITE_EXACTNESS
C++ version
Compiled on Mar 12 2020 at 16:04:11.
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 = 10
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 = 10
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] = 4.310652630718288e-06
w[ 1] = 0.0007580709343122178
w[ 2] = 0.01911158050077029
w[ 3] = 0.1354837029802677
w[ 4] = 0.3446423349320192
w[ 5] = 0.3446423349320192
w[ 6] = 0.1354837029802677
w[ 7] = 0.01911158050077029
w[ 8] = 0.0007580709343122178
w[ 9] = 4.310652630718288e-06
Abscissas X:
x[ 0] = -4.859462828332313
x[ 1] = -3.581823483551928
x[ 2] = -2.484325841638955
x[ 3] = -1.465989094391158
x[ 4] = -0.4849357075154977
x[ 5] = 0.4849357075154977
x[ 6] = 1.465989094391158
x[ 7] = 2.484325841638955
x[ 8] = 3.581823483551928
x[ 9] = 4.859462828332313
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
6 5.921189464667501e-16
7 8.326672684688674e-16
8 1.353414734781143e-15
9 9.769962616701378e-15
10 2.285767107630375e-15
HERMITE_EXACTNESS:
Normal end of execution.
12 March 2020 04:11:01 PM