19 December 2011 03:24:02 PM

CHEBYSHEV_PRB
  C++ version
  Test the CHEBYSHEV library.

CHEBYSHEV_TEST01
  CHEBYSHEV_COEFFICIENTS computes the coefficients of the
  Chebyshev interpolant.
  CHEBYSHEV_INTERPOLANT evaluates the interpolant.

  F(X) is a trig function:

          X               C(I)            F(X)           C(F)(X)

       -0.951057    -3.77476e-16       -0.424215       -0.424215
       -0.587785        0.593826       -0.576453       -0.576453
     6.12323e-17     4.44089e-17     5.77101e-16     6.78476e-16
        0.587785       -0.239113        0.576453        0.576453
        0.951057     7.66054e-16        0.424215        0.424215

  Consider the same F(X), but now over [0,3]:

          X               C(I)            F(X)           C(F)(X)

       0.0734152        0.316211        0.571335        0.571335
        0.618322     7.10543e-16        0.323929        0.323929
             1.5        0.689696              -1              -1
         2.38168    -1.11022e-15        0.323929        0.323929
         2.92658       -0.468409        0.571335        0.571335

  Consider the same F(X), but now with higher order:

          X               C(I)            F(X)           C(F)(X)

       -0.987688    -6.88338e-16       -0.115428       -0.115428
       -0.891007        0.446342         -0.6629         -0.6629
       -0.707107     1.08247e-16       0.0990411       0.0990411
        -0.45399       -0.333248       -0.869792       -0.869792
       -0.156434    -6.05072e-16       -0.552029       -0.552029
        0.156434        0.275317        0.552029        0.552029
         0.45399      1.4988e-16        0.869792        0.869792
        0.707107       -0.411266      -0.0990411      -0.0990411
        0.891007    -5.21805e-16          0.6629          0.6629
        0.987688       -0.233073        0.115428        0.115428

  F(X) is a degree 4 polynomial:

          X               C(I)            F(X)           C(F)(X)

       -0.987688          -14.25        -15.9489        -15.9489
       -0.891007            8.75        -15.4304        -15.4304
       -0.707107              -1        -13.9675        -13.9675
        -0.45399           -0.75         -11.289         -11.289
       -0.156434           0.125        -7.78211        -7.78211
        0.156434     5.68434e-15        -4.36352        -4.36352
         0.45399      7.4607e-15        -1.86266        -1.86266
        0.707107    -2.66454e-15       -0.532486       -0.532486
        0.891007    -3.55271e-16      -0.0724311      -0.0724311
        0.987688    -1.02141e-14    -0.000911305    -0.000911305

  The polynomial approximation to F(X) decays:

          X               C(I)            F(X)           C(F)(X)

       -0.987688         2.53213        0.372437        0.372437
       -0.891007         1.13032        0.410243        0.410243
       -0.707107        0.271495        0.493069        0.493069
        -0.45399       0.0443368        0.635089        0.635089
       -0.156434      0.00547424        0.855188        0.855188
        0.156434     0.000542926         1.16933         1.16933
         0.45399     4.49773e-05         1.57458         1.57458
        0.707107     3.19844e-06         2.02811         2.02811
        0.891007     1.99211e-07         2.43758         2.43758
        0.987688     1.10118e-08         2.68502         2.68502

CHEBYSHEV_PRB
  Normal end of execution.

19 December 2011 03:24:02 PM