24 January 2008 12:00:36 PM INT_EXACTNESS_GEN_HERMITE C++ version Investigate the polynomial exactness of a generalized Gauss-Hermite quadrature rule by integrating exponentially weighted monomials up to a given degree over the (-oo,+oo) interval. INT_EXACTNESS_GEN_HERMITE: User input: Quadrature rule X file = "gen_herm_o2_a1.0_modified_x.txt". Quadrature rule W file = "gen_herm_o2_a1.0_modified_w.txt". Quadrature rule R file = "gen_herm_o2_a1.0_modified_r.txt". Maximum degree to check = 5 Power of |X|, ALPHA = 1 OPTION = 1, integrate f(x) Spatial dimension = 1 Number of points = 2 The quadrature rule to be tested is a generalized Gauss-Hermite rule ORDER = 2 ALPHA = 1 OPTION = 1: Modified rule: Integral ( -oo < x < +oo ) f(x) dx is to be approximated by sum ( 1 <= I <= ORDER ) w(i) * f(x(i)). Weights W: w[ 0] = 1.359140914229523 w[ 1] = 1.359140914229523 Abscissas X: x[ 0] = -1 x[ 1] = 1 Region R: r[ 0] = -1e+30 r[ 1] = 1e+30 A generalized Gauss-Hermite rule would be able to exactly integrate monomials up to and including degree = 3 Error Degree 2.220446049250313e-16 0 0 1 2.220446049250313e-16 2 0 3 0.4999999999999999 4 0 5 INT_EXACTNESS_GEN_HERMITE: Normal end of execution. 24 January 2008 12:00:36 PM