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