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13-May-2025 15:27:11

line_fekete_rule_test():
  MATLAB/Octave version 9.11.0.2358333 (R2021b) Update 7
  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:
   -1.0000   -0.6637   -0.0070    0.6416    1.0000

  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:
   -1.0000   -0.6637   -0.0070    0.6416    1.0000


  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
         989
        2516
        4055
        5001


  NF = 5

  Estimated Fekete points XF:
   -1.0000   -0.6048    0.0060    0.6216    1.0000


  Graphics saved as "line_fekete_legendre.png"

  Sum(WF) = 2

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

  NF = 5

  Estimated Fekete points XF:
   -1.0000
   -0.6560
         0
    0.6248
    1.0000


  Graphics saved as "line_fekete_monomial.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 7

   -1.0000   -0.9379   -0.7918   -0.5736   -0.2993   -0.0030    0.2993

  Columns 8 through 11

    0.5696    0.7898    0.9379    1.0000

  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 7

   -1.0000   -0.9379   -0.7918   -0.5736   -0.2993   -0.0030    0.2993

  Columns 8 through 11

    0.5696    0.7898    0.9379    1.0000


  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 7

   -1.0000   -0.9224   -0.7388   -0.5464   -0.2948   -0.0056    0.2796

  Columns 8 through 11

    0.5412    0.7380    0.9216    1.0000


  Graphics saved as "line_fekete_legendre.png"

  Sum(WF) = 2

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

  NF = 11

  Estimated Fekete points XF:
   -1.0000
   -0.8996
   -0.7056
   -0.5676
   -0.4124
   -0.0460
    0.3084
    0.4948
    0.6512
    0.8868
    1.0000


  Graphics saved as "line_fekete_monomial.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 7

   -1.0000   -0.9840   -0.9439   -0.8819   -0.7998   -0.6997   -0.5816

  Columns 8 through 14

   -0.4494   -0.3073   -0.1572   -0.0010    0.1532    0.3053    0.4494

  Columns 15 through 21

    0.5816    0.6997    0.8018    0.8839    0.9439    0.9840    1.0000

  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 7

   -1.0000   -0.9840   -0.9439   -0.8819   -0.7998   -0.6997   -0.5816

  Columns 8 through 14

   -0.4494   -0.3073   -0.1572   -0.0010    0.1532    0.3053    0.4494

  Columns 15 through 21

    0.5816    0.6997    0.8018    0.8839    0.9439    0.9840    1.0000


  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 7

   -1.0000   -0.9784   -0.9260   -0.8712   -0.7948   -0.7016   -0.6128

  Columns 8 through 14

   -0.4060   -0.2864   -0.1480   -0.0012    0.1460    0.2908    0.4208

  Columns 15 through 21

    0.5424    0.6312    0.7944    0.8708    0.9260    0.9784    1.0000


  Graphics saved as "line_fekete_legendre.png"

  Sum(WF) = 2

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

  NF = 21

  Estimated Fekete points XF:
   -1.0000
   -0.9816
   -0.9500
   -0.8932
   -0.8324
   -0.7228
   -0.5588
   -0.4528
   -0.3268
   -0.1552
    0.0132
    0.1692
    0.3184
    0.4524
    0.5972
    0.7368
    0.8380
    0.8968
    0.9516
    0.9824
    1.0000


  Graphics saved as "line_fekete_monomial.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 7

   -1.0000   -0.9960   -0.9860   -0.9700   -0.9479   -0.9199   -0.8879

  Columns 8 through 14

   -0.8498   -0.8058   -0.7578   -0.7037   -0.6476   -0.5856   -0.5215

  Columns 15 through 21

   -0.4535   -0.3834   -0.3093   -0.2352   -0.1572   -0.0811   -0.0010

  Columns 22 through 28

    0.0771    0.1572    0.2332    0.3093    0.3814    0.4535    0.5215

  Columns 29 through 35

    0.5856    0.6476    0.7037    0.7578    0.8058    0.8498    0.8879

  Columns 36 through 41

    0.9199    0.9479    0.9700    0.9860    0.9960    1.0000

  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 7

   -1.0000   -0.9960   -0.9860   -0.9700   -0.9479   -0.9199   -0.8879

  Columns 8 through 14

   -0.8498   -0.8058   -0.7578   -0.7037   -0.6476   -0.5856   -0.5215

  Columns 15 through 21

   -0.4535   -0.3834   -0.3093   -0.2352   -0.1572   -0.0811   -0.0010

  Columns 22 through 28

    0.0771    0.1572    0.2332    0.3093    0.3814    0.4535    0.5215

  Columns 29 through 35

    0.5856    0.6476    0.7037    0.7578    0.8058    0.8498    0.8879

  Columns 36 through 41

    0.9199    0.9479    0.9700    0.9860    0.9960    1.0000


  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
         312
         406
         505
         620
         752
         894
        1035
        1157
        1443
        1592
        1770
        1942
        2122
        2305
        2478
        2671
        2831
        3157
        3303
        3490
        3640
        3796
        3960
        4117
        4252
        4380
        4496
        4596
        4691
        4758
        4866
        4916
        4952
        4987
        5001


  NF = 41

  Estimated Fekete points XF:
  Columns 1 through 7

   -1.0000   -0.9944   -0.9804   -0.9660   -0.9460   -0.9028   -0.8756

  Columns 8 through 14

   -0.8380   -0.7984   -0.7524   -0.6996   -0.6428   -0.5864   -0.5376

  Columns 15 through 21

   -0.4232   -0.3636   -0.2924   -0.2236   -0.1516   -0.0784   -0.0092

  Columns 22 through 28

    0.0680    0.1320    0.2624    0.3208    0.3956    0.4556    0.5180

  Columns 29 through 35

    0.5836    0.6464    0.7004    0.7516    0.7980    0.8380    0.8760

  Columns 36 through 41

    0.9028    0.9460    0.9660    0.9804    0.9944    1.0000


  Graphics saved as "line_fekete_legendre.png"

  Sum(WF) = 2

line_fekete_monomial_test():
  Seek Fekete points in [-1,1]
  using 5001 equally spaced sample points
  for polynomials of degree M = 41
  using the monomial basis and uniform weight.
[Warning: Rank deficient, rank = 36, tol =  7.110318e-12.] 
[> In line_fekete_monomial (line 81)
In line_fekete_monomial_test (line 46)
In line_fekete_rule_test (line 31)
In run (line 91)
] 

  NF = 36

  Estimated Fekete points XF:
   -1.0000
   -0.9912
   -0.9756
   -0.9480
   -0.9184
   -0.8920
   -0.8596
   -0.8164
   -0.7712
   -0.6964
   -0.5908
   -0.5328
   -0.4716
   -0.4004
   -0.3292
   -0.2560
   -0.1764
   -0.0284
    0.0372
    0.1052
    0.2380
    0.3648
    0.4256
    0.4888
    0.5712
    0.6532
    0.7344
    0.7760
    0.8120
    0.8740
    0.9176
    0.9488
    0.9740
    0.9908
    0.9968
    1.0000


  Graphics saved as "line_fekete_monomial.png"

  Sum(WF) = 2

line_fekete_rule_test():
  Normal end of execution.

13-May-2025 15:27:20