28 February 2022 03:21:20 PM
quadrature_golub_welsch_test():
C version
Test quadrature_golub_welsch().
TEST01:
Compute points and weights for Gauss quadrature
with the Chebyshev Type 1 weight w(x) = 1/sqrt(1-x^2).
Order N = 5
Interval = [-1,1]
Abscissas:
0 -0.951057
1 -0.587785
2 2.26221e-18
3 0.587785
4 0.951057
Weights:
0 0.628319
1 0.628319
2 0.628319
3 0.628319
4 0.628319
TEST02:
Compute points and weights for Gauss quadrature
with the Chebyshev Type 2 weight w(x) = sqrt(1-x^2).
Order N = 5
Interval = [-1,1]
Abscissas:
0 -0.866025
1 -0.5
2 5.95249e-17
3 0.5
4 0.866025
Weights:
0 0.1309
1 0.392699
2 0.523599
3 0.392699
4 0.1309
TEST03:
Compute points and weights for Gauss quadrature
with the Gegenbauer weight w(x) = (1-x^2)^alpha.
Order N = 5
ALPHA = 0.25
Interval = [-1,1]
Abscissas:
0 -0.885526
1 -0.518146
2 6.84469e-18
3 0.518146
4 0.885526
Weights:
0 0.171047
1 0.43055
2 0.544843
3 0.43055
4 0.171047
TEST04:
Compute points and weights for Gauss quadrature
with the generalized Hermite weight w(x) = |x|^alpha * exp(-x^2).
ALPHA = 2
Order N = 5
Interval = (-oo,+oo)
Abscissas:
0 -2.3175
1 -1.27639
2 5.11203e-16
3 1.27639
4 2.3175
Weights:
0 0.0288027
1 0.313028
2 0.202566
3 0.313028
4 0.0288027
TEST05:
Compute points and weights for Gauss quadrature
with the generalized Laguerre weight w(x) = x^alpha * exp(-x).
Order N = 5
ALPHA = 2
Interval = [0,+oo)
Abscissas:
0 1.03111
1 2.83721
2 5.62029
3 9.68291
4 15.8285
Weights:
0 0.520917
1 1.06671
2 0.38355
3 0.0285642
4 0.000262713
TEST06:
Compute points and weights for Gauss quadrature
with the Hermite weight w(x) = exp(-x^2).
Order N = 5
Interval = (-oo,+oo)
Abscissas:
0 -2.02018
1 -0.958572
2 2.40258e-16
3 0.958572
4 2.02018
Weights:
0 0.0199532
1 0.393619
2 0.945309
3 0.393619
4 0.0199532
TEST07:
Compute points and weights for Gauss quadrature
with the Jacobi weight w(x) = (1-x^2)^alpha*(1+x)^beta
Order N = 5
ALPHA = 0.25
BETA = 0.75
Interval = [-1,1]
Abscissas:
0 -0.835553
1 -0.446113
2 0.062007
3 0.552614
4 0.894318
Weights:
0 0.0874589
1 0.330899
2 0.538382
3 0.495706
4 0.213635
TEST08:
Compute points and weights for Gauss quadrature
with the Laguerre weight w(x) = exp(-x).
Order N = 5
Interval = [0,+oo)
Abscissas:
0 0.26356
1 1.4134
2 3.59643
3 7.08581
4 12.6408
Weights:
0 0.521756
1 0.398667
2 0.0759424
3 0.00361176
4 2.337e-05
TEST09:
Compute points and weights for Gauss quadrature
with the Legendre weight w(x) = 1.
Order N = 5
Interval = [-1,1]
Abscissas:
0 -0.90618
1 -0.538469
2 -1.08185e-16
3 0.538469
4 0.90618
Weights:
0 0.236927
1 0.478629
2 0.568889
3 0.478629
4 0.236927
QWGW_TEST:
Normal end of execution.
28 February 2022 03:21:20 PM
C 代码 使用 计算高斯正交规则的点和权重 戈鲁布-韦尔施程序.rar
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