08-Jan-2022 07:59:01

quadrature_golub_welsch_test():
  MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2
  Test quadrature_golub_welsch().

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:

     1:    -0.951057
     2:    -0.587785
     3:  2.26221e-18
     4:     0.587785
     5:     0.951057

  Weights:

     1:     0.628319
     2:     0.628319
     3:     0.628319
     4:     0.628319
     5:     0.628319

a =

    -1


quadrature_golub_welsch_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:

     1:    -0.866025
     2:         -0.5
     3:  5.95249e-17
     4:          0.5
     5:     0.866025

  Weights:

     1:       0.1309
     2:     0.392699
     3:     0.523599
     4:     0.392699
     5:       0.1309

quadrature_golub_welsch_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:

     1:    -0.885526
     2:    -0.518146
     3:  6.84469e-18
     4:     0.518146
     5:     0.885526

  Weights:

     1:     0.171047
     2:      0.43055
     3:     0.544843
     4:      0.43055
     5:     0.171047

quadrature_golub_welsch_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)

bj =

    1.2247
    1.0000
    1.5811
    1.4142
         0


mu0 =

    0.8862


  Abscissas:

     1:      -2.3175
     2:     -1.27639
     3:  5.11203e-16
     4:      1.27639
     5:       2.3175

  Weights:

     1:    0.0288027
     2:     0.313028
     3:     0.202566
     4:     0.313028
     5:    0.0288027

quadrature_golub_welsch_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)

mu0 =

     2


  Abscissas:

     1:      1.03111
     2:      2.83721
     3:      5.62029
     4:      9.68291
     5:      15.8285

  Weights:

     1:     0.520917
     2:      1.06671
     3:      0.38355
     4:    0.0285642
     5:  0.000262713

quadrature_golub_welsch_test06:
  Compute points and weights for Gauss quadrature
  with the Hermite weight w(x) = exp(-x^2).
  Order N = 5
  Interval = (-oo,+oo)

bj =

    0.5000
         0
         0
         0
         0


bj =

    0.5000
    1.0000
         0
         0
         0


bj =

    0.5000
    1.0000
    1.5000
         0
         0


bj =

    0.5000
    1.0000
    1.5000
    2.0000
         0


  Abscissas:

     1:     -2.02018
     2:    -0.958572
     3:  2.40258e-16
     4:     0.958572
     5:      2.02018

  Weights:

     1:    0.0199532
     2:     0.393619
     3:     0.945309
     4:     0.393619
     5:    0.0199532

quadrature_golub_welsch_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:

     1:    -0.835553
     2:    -0.446113
     3:     0.062007
     4:     0.552614
     5:     0.894318

  Weights:

     1:    0.0874589
     2:     0.330899
     3:     0.538382
     4:     0.495706
     5:     0.213635

quadrature_golub_welsch_test08:
  Compute points and weights for Gauss quadrature
  with the Laguerre weight w(x) = exp(-x).
  Order N = 5
  Interval = [0,+oo)

  Abscissas:

     1:      0.26356
     2:       1.4134
     3:      3.59643
     4:      7.08581
     5:      12.6408

  Weights:

     1:     0.521756
     2:     0.398667
     3:    0.0759424
     4:   0.00361176
     5:    2.337e-05

quadrature_golub_welsch_test09:
  Compute points and weights for Gauss quadrature
  with the Legendre weight w(x) = 1.
  Order N = 5
  Interval = [-1,1]

  Abscissas:

     1:     -0.90618
     2:    -0.538469
     3: -1.08185e-16
     4:     0.538469
     5:      0.90618

  Weights:

     1:     0.236927
     2:     0.478629
     3:     0.568889
     4:     0.478629
     5:     0.236927

quadrature_golub_welsch_test():
  Normal end of execution.

08-Jan-2022 07:59:01