13-Feb-2019 10:06:00

lebesgue_test
  MATLAB version
  Test the LEBESGUE library.

LEBESGUE_CHEBYSHEV1_TEST:
  Analyze Chebyshev1 points.

  Chebyshev1 Lebesgue constants:

     1:            1
     2:      1.41421
     3:      1.66667
     4:      1.84776
     5:      1.98885
     6:       2.1044
     7:      2.20221
     8:      2.28702
     9:      2.36186
    10:      2.42883
    11:      2.48943
    12:      2.54477
    13:      2.59568
    14:      2.64282
    15:      2.68671
    16:      2.72778
    17:      2.76635
    18:      2.80273
    19:      2.83713
    20:      2.86977
    21:      2.90082

  Chebyshev1 Lebesgue constants/log(N+1):

     1:       1.4427
     2:      1.28727
     3:      1.20225
     4:      1.14808
     5:         1.11
     6:      1.08145
     7:      1.05904
     8:      1.04087
     9:      1.02574
    10:       1.0129
    11:      1.00182
    12:     0.992131
    13:     0.983563
    14:     0.975913
    15:     0.969028
    16:     0.962786
    17:     0.957093
    18:     0.951871
    19:     0.947058
    20:     0.942602
    21:     0.938462

  Chebyshev1 points for N = 11

     1:     0.989821
     2:     0.909632
     3:      0.75575
     4:     0.540641
     5:     0.281733
     6:  2.83277e-16
     7:    -0.281733
     8:    -0.540641
     9:     -0.75575
    10:    -0.909632
    11:    -0.989821

  Plot file saved as "chebyshev1.png"

LEBESGUE_CHEBYSHEV2_TEST:
  Analyze Chebyshev2 points.

  Chebyshev2 Lebesgue constants for N = 1 to 11:

     1:            1
     2:            1
     3:         1.25
     4:      1.66667
     5:      1.79876
     6:      1.98885
     7:      2.08255
     8:      2.20221
     9:      2.27461
    10:      2.36186
    11:      2.42097

  Chebyshev2 Lebesgue constants/log(N+1):

     1:       1.4427
     2:     0.910239
     3:     0.901684
     4:      1.03556
     5:      1.00391
     6:      1.02207
     7:      1.00149
     8:      1.00227
     9:     0.987852
    10:     0.984971
    11:     0.974269

  Chebyshev2 points for N = 11

     1:           -1
     2:    -0.951057
     3:    -0.809017
     4:    -0.587785
     5:    -0.309017
     6:  6.12323e-17
     7:     0.309017
     8:     0.587785
     9:     0.809017
    10:     0.951057
    11:            1

  Plot file saved as "chebyshev2.png"

LEBESGUE_CHEBYSHEV3_TEST:
  Analyze Chebyshev3 points.

  Chebyshev3 Lebesgue constants for N = 1 to 11:

     1:            1
     2:      2.23607
     3:      3.49396
     4:      4.75877
     5:      6.02667
     6:      7.29623
     7:      8.56677
     8:      9.83795
     9:      11.1096
    10:      12.3815
    11:      13.6536

  Chebyshev3 Lebesgue constants/log(N+1):

     1:       1.4427
     2:      2.03536
     3:      2.52036
     4:      2.95679
     5:      3.36355
     6:      3.74952
     7:      4.11975
     8:      4.47744
     9:      4.82482
    10:      5.16348
    11:      5.49463

  Chebyshev3 points for N = 11

     1:    -0.962917
     2:    -0.854419
     3:    -0.682553
     4:    -0.460065
     5:    -0.203456
     6:    0.0682424
     7:      0.33488
     8:      0.57668
     9:     0.775711
    10:     0.917211
    11:     0.990686

  Plot file saved as "chebyshev3.png"

LEBESGUE_CHEBYSHEV4_TEST:
  Analyze Chebyshev4 points.

  Chebyshev4 Lebesgue constants for N = 1 to 11:

     1:            1
     2:      2.23607
     3:      3.49396
     4:      4.75877
     5:      6.02667
     6:      7.29623
     7:      8.56677
     8:      9.83795
     9:      11.1096
    10:      12.3815
    11:      13.6536

  Chebyshev4 Lebesgue constants/log(N+1):

     1:       1.4427
     2:      2.03536
     3:      2.52036
     4:      2.95679
     5:      3.36355
     6:      3.74952
     7:      4.11975
     8:      4.47744
     9:      4.82482
    10:      5.16348
    11:      5.49463

  Chebyshev4 points for N = 11

     1:    -0.990686
     2:    -0.917211
     3:    -0.775711
     4:     -0.57668
     5:     -0.33488
     6:   -0.0682424
     7:     0.203456
     8:     0.460065
     9:     0.682553
    10:     0.854419
    11:     0.962917

  Plot file saved as "s"

LEBESGUE_EQUIDISTANT1_TEST:
  Analyze Equidistant1 points.

  Equidistant1 Lebesgue constants for N = 1 to 11:

     1:            1
     2:            3
     3:            7
     4:           15
     5:           31
     6:           63
     7:          127
     8:          255
     9:          511
    10:         1023
    11:         2047

  Equidistant1 points for N = 11

     1:    -0.833333
     2:    -0.666667
     3:         -0.5
     4:    -0.333333
     5:    -0.166667
     6:            0
     7:     0.166667
     8:     0.333333
     9:          0.5
    10:     0.666667
    11:     0.833333

  Plot file saved as "equidistant1.png"

LEBESGUE_EQUIDISTANT2_TEST:
  Analyze Equidistant2 points.

  Equidistant2 Lebesgue constants for N = 1 to 11:

     1:            1
     2:            1
     3:         1.25
     4:      1.63112
     5:      2.20782
     6:      3.10628
     7:      4.54872
     8:      6.92945
     9:      10.9444
    10:      17.8449
    11:      29.8907

  Equidistant2 points for N = 11

     1:           -1
     2:         -0.8
     3:         -0.6
     4:         -0.4
     5:         -0.2
     6:            0
     7:          0.2
     8:          0.4
     9:          0.6
    10:          0.8
    11:            1

  Plot file saved as "equidistant2.png"

LEBESGUE_EQUIDISTANT3_TEST:
  Analyze Equidistant3 points.

  Equidistant3 Lebesgue constants for N = 1 to 11:

     1:            1
     2:            2
     3:          3.5
     4:            6
     5:       10.375
     6:        18.25
     7:      32.6875
     8:         59.5
     9:      109.773
    10:      204.734
    11:       385.16

  Equidistant3 points for N = 11

     1:    -0.909091
     2:    -0.727273
     3:    -0.545455
     4:    -0.363636
     5:    -0.181818
     6:            0
     7:     0.181818
     8:     0.363636
     9:     0.545455
    10:     0.727273
    11:     0.909091

  Plot file saved as "equidistant3.png"

LEBESGUE_FEJER1_TEST:
  Analyze Fejer1 points.

  Fejer1 Lebesgue constants for N = 1 to 11:

     1:            1
     2:      1.41421
     3:      1.66667
     4:      1.84776
     5:      1.98885
     6:       2.1044
     7:      2.20221
     8:      2.28702
     9:      2.36186
    10:      2.42883
    11:      2.48943

  Fejer1 points for N = 11

     1:    -0.989821
     2:    -0.909632
     3:     -0.75575
     4:    -0.540641
     5:    -0.281733
     6: -1.60812e-16
     7:     0.281733
     8:     0.540641
     9:      0.75575
    10:     0.909632
    11:     0.989821

  Plot file saved as "fejer1.png"

LEBESGUE_FEJER2_TEST:
  Analyze Fejer2 points.

  Fejer2 Lebesgue constants for N = 1 to 11:

     1:            1
     2:            2
     3:            3
     4:            4
     5:            5
     6:            6
     7:            7
     8:            8
     9:            9
    10:           10
    11:           11

  Fejer2 points for N = 11

     1:    -0.965926
     2:    -0.866025
     3:    -0.707107
     4:         -0.5
     5:    -0.258819
     6:  2.83277e-16
     7:     0.258819
     8:          0.5
     9:     0.707107
    10:     0.866025
    11:     0.965926

  Plot file saved as "fejer2.png"

lebesgue_test
  Normal end of execution.

13-Feb-2019 10:06:02