10-Nov-2022 11:49:52

bernstein_approximation_test():
  MATLAB/Octave version 4.2.2
  Test bernstein_approximation().

bernstein_poly_ab_approx_test():
  bernstein_poly_ab_approx() evaluates the Bernstein polynomial
  approximant to a function F(X).
  As N, the polynomial degree increases, the norm of the error
  should decrease.

  Approximate y=sin(x) over the interval [1,3]

   N         |F-B| / |F|

   0        0.815433
   1        0.357447
   2        0.175581
   3        0.117312
   4       0.0882046
   5       0.0707012
   6        0.059005
   7       0.0506338
   8       0.0443449
   9       0.0394468
  10       0.0355237
  11       0.0323107
  12        0.029631
  13       0.0273619
  14       0.0254157
  15        0.023728
  16       0.0222506
  17       0.0209464
  18       0.0197867
  19       0.0187486
  20       0.0178141

  Approximate y=heaviside(x) over the interval [-1,+1]

   N         |F-B| / |F|

   0               1
   1        0.497006
   2        0.497006
   3        0.372257
   4        0.372257
   5        0.309883
   6        0.309883
   7        0.270899
   8        0.270899
   9         0.24361
  10         0.24361
  11        0.223143
  12        0.223143
  13        0.207062
  14        0.207062
  15        0.193997
  16        0.193997
  17        0.183109
  18        0.183109
  19        0.173854
  20        0.173854

bernstein_poly_ab_approx_display():
  bernstein_poly_ab_approx() evaluates the Bernstein polynomial
  approximant to a function F(X).

  This program displays the sequence of approximants
  to y=sin(x) over the interval [1,3]
  Graphics saved as "bernstein_sine_00"
  Graphics saved as "bernstein_sine_01"
  Graphics saved as "bernstein_sine_02"
  Graphics saved as "bernstein_sine_03"
  Graphics saved as "bernstein_sine_04"
  Graphics saved as "bernstein_sine_05"
  Graphics saved as "bernstein_sine_06"
  Graphics saved as "bernstein_sine_07"
  Graphics saved as "bernstein_sine_08"
  Graphics saved as "bernstein_sine_09"
  Graphics saved as "bernstein_sine_10"
  Graphics saved as "bernstein_heaviside_01"
  Graphics saved as "bernstein_heaviside_03"
  Graphics saved as "bernstein_heaviside_05"
  Graphics saved as "bernstein_heaviside_07"
  Graphics saved as "bernstein_heaviside_09"
  Graphics saved as "bernstein_heaviside_11"
  Graphics saved as "bernstein_heaviside_13"
  Graphics saved as "bernstein_heaviside_15"
  Graphics saved as "bernstein_heaviside_17"
  Graphics saved as "bernstein_heaviside_19"

bernstein_approximation_test():
  Normal end of execution.

10-Nov-2022 11:50:57