15-May-2025 08:57:34

line_fekete_rule_test():
  MATLAB/Octave version 6.4.0
  Test line_fekete_rule().

line_fekete_bos_levenberg_test():
  Seek Fekete points in [-1,1]
  using 1000 equally spaced sample points
  for polynomial space of dimension M = 5
  with the Chebyshev basis
  and weight 1/sqrt(1-x^2).

  Estimated Fekete points XF:
  -1.0000e+00  -6.6366e-01  -7.0070e-03   6.4164e-01   1.0000e+00
  Graphics saved as "line_fekete_bos_levenberg.png"

line_fekete_chebyshev_test():
  Seek Fekete points in [-1,1]
  using 1000 equally spaced sample points
  for polynomials of degree M = 5
  with the Chebyshev basis
  and weight 1/sqrt(1-x^2).

  NF = 5

  Estimated Fekete points XF:
  -1.0000e+00  -6.6366e-01  -7.0070e-03   6.4164e-01   1.0000e+00

  Graphics saved as "line_fekete_chebyshev.png"

  Sum(WF) = 3.14159

line_fekete_legendre_test():
  Seek Fekete points in [-1,1]
  using 5001 equally spaced sample points
  for polynomials of degree M = 5
  with the Legendre basis and uniform weight.
ind =

      1
    947
   2486
   4013
   5001


  NF = 5

  Estimated Fekete points XF:
  -1.0000e+00  -6.2160e-01  -6.0000e-03   6.0480e-01   1.0000e+00

  Graphics saved as "line_fekete_legendre.png"

  Sum(WF) = 2

line_fekete_bos_levenberg_test():
  Seek Fekete points in [-1,1]
  using 1000 equally spaced sample points
  for polynomial space of dimension M = 11
  with the Chebyshev basis
  and weight 1/sqrt(1-x^2).

  Estimated Fekete points XF:
 Columns 1 through 6:

  -1.0000e+00  -9.3794e-01  -7.9179e-01  -5.7357e-01  -2.9930e-01  -3.0030e-03

 Columns 7 through 11:

   2.9930e-01   5.6957e-01   7.8979e-01   9.3794e-01   1.0000e+00
  Graphics saved as "line_fekete_bos_levenberg.png"

line_fekete_chebyshev_test():
  Seek Fekete points in [-1,1]
  using 1000 equally spaced sample points
  for polynomials of degree M = 11
  with the Chebyshev basis
  and weight 1/sqrt(1-x^2).

  NF = 11

  Estimated Fekete points XF:
 Columns 1 through 6:

  -1.0000e+00  -9.3794e-01  -7.9179e-01  -5.7357e-01  -2.9930e-01  -3.0030e-03

 Columns 7 through 11:

   2.9930e-01   5.6957e-01   7.8979e-01   9.3794e-01   1.0000e+00

  Graphics saved as "line_fekete_chebyshev.png"

  Sum(WF) = 3.14159

line_fekete_legendre_test():
  Seek Fekete points in [-1,1]
  using 5001 equally spaced sample points
  for polynomials of degree M = 11
  with the Legendre basis and uniform weight.
ind =

      1
    195
    654
   1135
   1764
   2487
   3200
   3854
   4346
   4805
   5001


  NF = 11

  Estimated Fekete points XF:
 Columns 1 through 6:

  -1.0000e+00  -9.2240e-01  -7.3880e-01  -5.4640e-01  -2.9480e-01  -5.6000e-03

 Columns 7 through 11:

   2.7960e-01   5.4120e-01   7.3800e-01   9.2160e-01   1.0000e+00

  Graphics saved as "line_fekete_legendre.png"

  Sum(WF) = 2

line_fekete_bos_levenberg_test():
  Seek Fekete points in [-1,1]
  using 1000 equally spaced sample points
  for polynomial space of dimension M = 21
  with the Chebyshev basis
  and weight 1/sqrt(1-x^2).

  Estimated Fekete points XF:
 Columns 1 through 6:

  -1.0000e+00  -9.8398e-01  -9.4394e-01  -8.8188e-01  -7.9980e-01  -6.9970e-01

 Columns 7 through 12:

  -5.8158e-01  -4.4945e-01  -3.0731e-01  -1.5716e-01  -1.0010e-03   1.5315e-01

 Columns 13 through 18:

   3.0531e-01   4.4945e-01   5.8158e-01   6.9970e-01   8.0180e-01   8.8388e-01

 Columns 19 through 21:

   9.4394e-01   9.8398e-01   1.0000e+00
  Graphics saved as "line_fekete_bos_levenberg.png"

line_fekete_chebyshev_test():
  Seek Fekete points in [-1,1]
  using 1000 equally spaced sample points
  for polynomials of degree M = 21
  with the Chebyshev basis
  and weight 1/sqrt(1-x^2).

  NF = 21

  Estimated Fekete points XF:
 Columns 1 through 6:

  -1.0000e+00  -9.8398e-01  -9.4394e-01  -8.8188e-01  -7.9980e-01  -6.9970e-01

 Columns 7 through 12:

  -5.8158e-01  -4.4945e-01  -3.0731e-01  -1.5716e-01  -1.0010e-03   1.5315e-01

 Columns 13 through 18:

   3.0531e-01   4.4945e-01   5.8158e-01   6.9970e-01   8.0180e-01   8.8388e-01

 Columns 19 through 21:

   9.4394e-01   9.8398e-01   1.0000e+00

  Graphics saved as "line_fekete_chebyshev.png"

  Sum(WF) = 3.14159

line_fekete_legendre_test():
  Seek Fekete points in [-1,1]
  using 5001 equally spaced sample points
  for polynomials of degree M = 21
  with the Legendre basis and uniform weight.
ind =

      1
     55
    186
    323
    514
    747
    969
   1486
   1785
   2131
   2498
   2866
   3228
   3553
   3857
   4079
   4487
   4678
   4816
   4947
   5001


  NF = 21

  Estimated Fekete points XF:
 Columns 1 through 6:

  -1.0000e+00  -9.7840e-01  -9.2600e-01  -8.7120e-01  -7.9480e-01  -7.0160e-01

 Columns 7 through 12:

  -6.1280e-01  -4.0600e-01  -2.8640e-01  -1.4800e-01  -1.2000e-03   1.4600e-01

 Columns 13 through 18:

   2.9080e-01   4.2080e-01   5.4240e-01   6.3120e-01   7.9440e-01   8.7080e-01

 Columns 19 through 21:

   9.2600e-01   9.7840e-01   1.0000e+00

  Graphics saved as "line_fekete_legendre.png"

  Sum(WF) = 2

line_fekete_bos_levenberg_test():
  Seek Fekete points in [-1,1]
  using 1000 equally spaced sample points
  for polynomial space of dimension M = 41
  with the Chebyshev basis
  and weight 1/sqrt(1-x^2).

  Estimated Fekete points XF:
 Columns 1 through 6:

  -1.0000e+00  -9.9600e-01  -9.8599e-01  -9.6997e-01  -9.4795e-01  -9.1992e-01

 Columns 7 through 12:

  -8.8789e-01  -8.4985e-01  -8.0581e-01  -7.5776e-01  -7.0370e-01  -6.4765e-01

 Columns 13 through 18:

  -5.8559e-01  -5.2152e-01  -4.5345e-01  -3.8338e-01  -3.0931e-01  -2.3524e-01

 Columns 19 through 24:

  -1.5716e-01  -8.1081e-02  -1.0010e-03   7.7077e-02   1.5716e-01   2.3323e-01

 Columns 25 through 30:

   3.0931e-01   3.8138e-01   4.5345e-01   5.2152e-01   5.8559e-01   6.4765e-01

 Columns 31 through 36:

   7.0370e-01   7.5776e-01   8.0581e-01   8.4985e-01   8.8789e-01   9.1992e-01

 Columns 37 through 41:

   9.4795e-01   9.6997e-01   9.8599e-01   9.9600e-01   1.0000e+00
  Graphics saved as "line_fekete_bos_levenberg.png"

line_fekete_chebyshev_test():
  Seek Fekete points in [-1,1]
  using 1000 equally spaced sample points
  for polynomials of degree M = 41
  with the Chebyshev basis
  and weight 1/sqrt(1-x^2).

  NF = 41

  Estimated Fekete points XF:
 Columns 1 through 6:

  -1.0000e+00  -9.9600e-01  -9.8599e-01  -9.6997e-01  -9.4795e-01  -9.1992e-01

 Columns 7 through 12:

  -8.8789e-01  -8.4985e-01  -8.0581e-01  -7.5776e-01  -7.0370e-01  -6.4765e-01

 Columns 13 through 18:

  -5.8559e-01  -5.2152e-01  -4.5345e-01  -3.8338e-01  -3.0931e-01  -2.3524e-01

 Columns 19 through 24:

  -1.5716e-01  -8.1081e-02  -1.0010e-03   7.7077e-02   1.5716e-01   2.3323e-01

 Columns 25 through 30:

   3.0931e-01   3.8138e-01   4.5345e-01   5.2152e-01   5.8559e-01   6.4765e-01

 Columns 31 through 36:

   7.0370e-01   7.5776e-01   8.0581e-01   8.4985e-01   8.8789e-01   9.1992e-01

 Columns 37 through 41:

   9.4795e-01   9.6997e-01   9.8599e-01   9.9600e-01   1.0000e+00

  Graphics saved as "line_fekete_chebyshev.png"

  Sum(WF) = 3.14159

line_fekete_legendre_test():
  Seek Fekete points in [-1,1]
  using 5001 equally spaced sample points
  for polynomials of degree M = 41
  with the Legendre basis and uniform weight.
ind =

      1
     15
     50
     86
    136
    244
    311
    406
    506
    622
    750
    885
   1042
   1206
   1362
   1512
   1699
   1845
   2171
   2331
   2524
   2697
   2880
   3060
   3232
   3410
   3559
   3845
   3967
   4108
   4250
   4382
   4497
   4596
   4690
   4758
   4866
   4916
   4952
   4987
   5001


  NF = 41

  Estimated Fekete points XF:
 Columns 1 through 6:

  -1.0000e+00  -9.9440e-01  -9.8040e-01  -9.6600e-01  -9.4600e-01  -9.0280e-01

 Columns 7 through 12:

  -8.7600e-01  -8.3800e-01  -7.9800e-01  -7.5160e-01  -7.0040e-01  -6.4640e-01

 Columns 13 through 18:

  -5.8360e-01  -5.1800e-01  -4.5560e-01  -3.9560e-01  -3.2080e-01  -2.6240e-01

 Columns 19 through 24:

  -1.3200e-01  -6.8000e-02   9.2000e-03   7.8400e-02   1.5160e-01   2.2360e-01

 Columns 25 through 30:

   2.9240e-01   3.6360e-01   4.2320e-01   5.3760e-01   5.8640e-01   6.4280e-01

 Columns 31 through 36:

   6.9960e-01   7.5240e-01   7.9840e-01   8.3800e-01   8.7560e-01   9.0280e-01

 Columns 37 through 41:

   9.4600e-01   9.6600e-01   9.8040e-01   9.9440e-01   1.0000e+00

  Graphics saved as "line_fekete_legendre.png"

  Sum(WF) = 2

line_fekete_rule_test():
  Normal end of execution.

15-May-2025 08:58:43