14-May-2025 11:21:52

cpr_test():
  MATLAB/Octave version 6.4.0
  Test cpr(), which uses the Chebyshev Proxy Rootfinder
  to determine all real zeros of a smooth function
  over an interval [a,b].

bessel_test():
  Seek real roots of the J0 Bessel function.

  Interstitial interpolation error norm = 8.77076e-15
  Number of roots = 12
  Roots computed by CPR:
    2.4048
    5.5201
    8.6537
   11.7915
   14.9309
   18.0711
   21.2116
   24.3525
   27.4935
   30.6346
   33.7758
   36.9171
  Maximum residual at roots = 1.01445e-14
  Exact roots:
    2.4048
    5.5201
    8.6537
   11.7915
   14.9309
   18.0711
   21.2116
   24.3525
   27.4935
   30.6346
   33.7758
   36.9171
  Exact f(roots):
  -1.0239e-16
  -1.4117e-17
   1.3004e-17
  -7.9654e-16
  -1.0152e-15
  -7.3745e-16
   7.5595e-17
  -7.2262e-16
   7.8726e-16
   5.8966e-16
   1.9964e-16
  -8.1131e-16
  f ( froots ):
   9.1641e-15
   4.9834e-15
  -8.3098e-15
   8.7343e-15
  -3.5014e-15
  -1.0144e-14
  -5.8862e-15
   6.1710e-15
   7.8159e-15
  -8.1171e-15
   8.0040e-15
   1.0549e-15

newton_test():
  Seek real roots of the Newton example x^3-2x-5=0.

  Interstitial interpolation error norm = 5.68434e-14
  Number of roots = 1
  Maximum residual at roots = 9.76996e-15
  Exact real root   :    2.094551481542328
  Computed real root:    2.094551481542327
  Exact f(roots)    :  1.4210854715202e-14
  Computed f(roots) : 9.769962616701378e-15
  Error             : 4.440892098500626e-16

jenkins_test():
  Seek real roots of the Jenkins polynomial
  p(x) = x^4 + 5.6562x^3 + 5.8854x^2
             + 7.3646x   + 6.1354

  Interstitial interpolation error norm = 4.54747e-13
  Maximum residual at roots = 2.08722e-13
  Number of roots = 2
  Computed roots:
  -4.674054017161708
  -0.999999999999975
  Exact roots:
  -4.674054017161709
  -1.000000000000000
  f (Computed roots ):
  -3.286260152890463e-14
   2.087219286295294e-13
  f(Exact roots):
  -1.865174681370263e-14
  -8.881784197001252e-16

cpr_test():
  Normal end of execution.
14-May-2025 11:21:52