C 代码 计算权重函数 rho（x） 的高斯正交规则 基于只需要知识的戈鲁布-韦尔施程序 的时刻 rho（x）.rar

21 January 2020 08:16:04 AM QUADMOM_TEST C version Test the QUADMOM library. QUADMOM_TEST01: Compute the points and weights of a quadrature rule for the Legendre weight, rho(x)=1, over [-1,+1], using Golub and Welsch's moment method. Compare with a standard calculation. Points from GW moment and orthogonal polynomial methods: 0: -0.906180 -0.90618 1: -0.538469 -0.538469 2: -0.000000 -1.08185e-16 3: 0.538469 0.538469 4: 0.906180 0.90618 Weights from GW moment and orthogonal polynomial methods: 0: 0.236927 0.236927 1: 0.478629 0.478629 2: 0.568889 0.568889 3: 0.478629 0.478629 4: 0.236927 0.236927 QUADMOM_TEST02: Compute the points and weights of a quadrature rule for the standard Gaussian weight, rho(x)=exp(-x^2/2)/sqrt(2pi), over (-oo,+oo), using Golub and Welsch's moment method. Compare with a standard calculation. Points from GW moment and orthogonal polynomial methods: 0: -2.856970 -2.85697 1: -1.355626 -1.35563 2: 0.000000 3.39776e-16 3: 1.355626 1.35563 4: 2.856970 2.85697 Weights from GW moment and orthogonal polynomial methods: 0: 0.011257 0.0112574 1: 0.222076 0.222076 2: 0.533333 0.533333 3: 0.222076 0.222076 4: 0.011257 0.0112574 QUADMOM_TEST03: Compute the points and weights of a quadrature rule for a general Gaussian weight, rho(mu,s;x)=exp(-((x-mu)/sigma)^2/2)/sigma^2/sqrt(2pi), over (-oo,+oo), using Golub and Welsch''s moment method. Compare with a standard calculation. MU = 1 SIGMA = 2 Points from GW moment and orthogonal polynomial methods: 0: -4.713940 -4.71394 1: -1.711252 -1.71125 2: 1.000000 1 3: 3.711252 3.71125 4: 6.713940 6.71394 Weights from GW moment and orthogonal polynomial methods: 0: 0.011257 0.0112574 1: 0.222076 0.222076 2: 0.533333 0.533333 3: 0.222076 0.222076 4: 0.011257 0.0112574 QUADMOM_TEST04: Compute the points and weights of a quadrature rule for the Laguerre weight, rho(x)=exp(-x), over [0,+oo), using Golub and Welsch's moment method. Compare with a standard calculation. Points from GW moment and orthogonal polynomial methods: 0: 0.263560 0.26356 1: 1.413403 1.4134 2: 3.596426 3.59643 3: 7.085810 7.08581 4: 12.640801 12.6408 Weights from GW moment and orthogonal polynomial methods: 0: 0.521756 0.521756 1: 0.398667 0.398667 2: 0.075942 0.0759424 3: 0.003612 0.00361176 4: 0.000023 2.337e-05 QUADMOM_TEST05: Compute the points and weights of a quadrature rule for a truncated normal weight, rho(mu,s;x)=exp(-((x-mu)/sigma)^2/2)/sigma^2/sqrt(2pi), over [a,b], using Golub and Welsch's moment method. MU = 100 SIGMA = 25 A = 50 B = 150 Points from GW moment method: 0 56.4761 1 76.3469 2 100 3 123.653 4 143.524 Weights from GW moment method: 0 0.0558883 1 0.242951 2 0.402322 3 0.242951 4 0.0558883 QUADMOM_TEST06: Compute the points and weights of a quadrature rule for a lower truncated normal weight, rho(mu,s;x)=exp(-((x-mu)/sigma)^2/2)/sigma^2/sqrt(2pi), over [a,+oo), using Golub and Welsch's moment method. MU = 2 SIGMA = 0.5 A = 0 Points from GW moment method: 0 0.181699 1 0.642167 2 1.13382 3 1.62238 4 2.10999 5 2.6048 6 3.11888 7 3.67288 8 4.31747 Weights from GW moment method: 0 0.000423598 1 0.00977389 2 0.0873214 3 0.292167 4 0.381303 5 0.192724 6 0.0345415 7 0.00173335 8 1.26241e-05 QUADMOM_TEST07: Compute the points and weights of a quadrature rule for a upper truncated normal weight, rho(mu,s;x)=exp(-((x-mu)/sigma)^2/2)/sigma^2/sqrt(2pi), over (-oo,b], using Golub and Welsch's moment method. MU = 2 SIGMA = 0.5 B = 3 Points from GW moment method: 0 -0.496845 1 0.120142 2 0.642856 3 1.11849 4 1.56329 5 1.98198 6 2.36954 7 2.70492 8 2.93754 Weights from GW moment method: 0 2.21118e-06 1 0.00038746 2 0.0101585 3 0.0791572 4 0.240687 5 0.330416 6 0.227969 7 0.0893336 8 0.0218891 QUADMOM_TEST08: Integrate sin(x) against a lower truncated normal weight. MU = 0 SIGMA = 1 A = -3 N Estimate 1 0.00443782 2 -0.00295694 3 0.000399622 4 -0.00023654 5 -0.000173932 6 -0.000177684 7 -0.000177529 8 -0.000177534 9 -0.000177534 QUADMOM_TEST Normal end of execution. 21 January 2020 08:16:04 AM