24-Oct-2022 18:32:40

line_fekete_rule_test():
  MATLAB/Octave version 4.2.2
  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:
  -1.0000000  -0.6636637  -0.0070070   0.6416416   1.0000000
  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:
  -1.0000000  -0.6636637  -0.0070070   0.6416416   1.0000000

  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:
  -1.0000000  -0.6216000  -0.0060000   0.6048000   1.0000000

  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:

  -1.0000000  -0.9379379  -0.7917918  -0.5735736  -0.2992993  -0.0030030

 Columns 7 through 11:

   0.2992993   0.5695696   0.7897898   0.9379379   1.0000000
  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:

  -1.0000000  -0.9379379  -0.7917918  -0.5735736  -0.2992993  -0.0030030

 Columns 7 through 11:

   0.2992993   0.5695696   0.7897898   0.9379379   1.0000000

  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:

  -1.0000000  -0.9224000  -0.7388000  -0.5464000  -0.2948000  -0.0056000

 Columns 7 through 11:

   0.2796000   0.5412000   0.7380000   0.9216000   1.0000000

  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:

  -1.0000000  -0.9839840  -0.9439439  -0.8818819  -0.7997998  -0.6996997

 Columns 7 through 12:

  -0.5815816  -0.4494494  -0.3073073  -0.1571572  -0.0010010   0.1531532

 Columns 13 through 18:

   0.3053053   0.4494494   0.5815816   0.6996997   0.8018018   0.8838839

 Columns 19 through 21:

   0.9439439   0.9839840   1.0000000
  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:

  -1.0000000  -0.9839840  -0.9439439  -0.8818819  -0.7997998  -0.6996997

 Columns 7 through 12:

  -0.5815816  -0.4494494  -0.3073073  -0.1571572  -0.0010010   0.1531532

 Columns 13 through 18:

   0.3053053   0.4494494   0.5815816   0.6996997   0.8018018   0.8838839

 Columns 19 through 21:

   0.9439439   0.9839840   1.0000000

  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:

  -1.0000000  -0.9784000  -0.9260000  -0.8712000  -0.7948000  -0.7016000

 Columns 7 through 12:

  -0.6128000  -0.4060000  -0.2864000  -0.1480000  -0.0012000   0.1460000

 Columns 13 through 18:

   0.2908000   0.4208000   0.5424000   0.6312000   0.7944000   0.8708000

 Columns 19 through 21:

   0.9260000   0.9784000   1.0000000

  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:

  -1.0000000  -0.9959960  -0.9859860  -0.9699700  -0.9479479  -0.9199199

 Columns 7 through 12:

  -0.8878879  -0.8498498  -0.8058058  -0.7577578  -0.7037037  -0.6476476

 Columns 13 through 18:

  -0.5855856  -0.5215215  -0.4534535  -0.3813814  -0.3093093  -0.2332332

 Columns 19 through 24:

  -0.1571572  -0.0770771   0.0010010   0.0810811   0.1571572   0.2352352

 Columns 25 through 30:

   0.3093093   0.3833834   0.4534535   0.5215215   0.5855856   0.6476476

 Columns 31 through 36:

   0.7037037   0.7577578   0.8058058   0.8498498   0.8878879   0.9199199

 Columns 37 through 41:

   0.9479479   0.9699700   0.9859860   0.9959960   1.0000000
  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:

  -1.0000000  -0.9959960  -0.9859860  -0.9699700  -0.9479479  -0.9199199

 Columns 7 through 12:

  -0.8878879  -0.8498498  -0.8058058  -0.7577578  -0.7037037  -0.6476476

 Columns 13 through 18:

  -0.5855856  -0.5215215  -0.4534535  -0.3813814  -0.3093093  -0.2332332

 Columns 19 through 24:

  -0.1571572  -0.0770771   0.0010010   0.0810811   0.1571572   0.2352352

 Columns 25 through 30:

   0.3093093   0.3833834   0.4534535   0.5215215   0.5855856   0.6476476

 Columns 31 through 36:

   0.7037037   0.7577578   0.8058058   0.8498498   0.8878879   0.9199199

 Columns 37 through 41:

   0.9479479   0.9699700   0.9859860   0.9959960   1.0000000

  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:

  -1.0000000  -0.9944000  -0.9804000  -0.9660000  -0.9460000  -0.9028000

 Columns 7 through 12:

  -0.8760000  -0.8380000  -0.7980000  -0.7516000  -0.7004000  -0.6464000

 Columns 13 through 18:

  -0.5836000  -0.5180000  -0.4556000  -0.3956000  -0.3208000  -0.2624000

 Columns 19 through 24:

  -0.1320000  -0.0680000   0.0092000   0.0784000   0.1516000   0.2236000

 Columns 25 through 30:

   0.2924000   0.3636000   0.4232000   0.5376000   0.5864000   0.6428000

 Columns 31 through 36:

   0.6996000   0.7524000   0.7984000   0.8380000   0.8756000   0.9028000

 Columns 37 through 41:

   0.9460000   0.9660000   0.9804000   0.9944000   1.0000000

  Graphics saved as "line_fekete_legendre.png"

  Sum(WF) = 2

line_fekete_rule_test():
  Normal end of execution.

24-Oct-2022 18:35:13