C 代码 检验高斯-埃尔米特正交规则的多项式精度.rar

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