toms446

toms446, an Octave code which implements ACM TOMS algorithm 446, for the manipulation of Chebyshev series, by Roger Broucke.

The text of many ACM TOMS algorithms is available online through ACM: https://calgo.acm.org/ or NETLIB: https://www.netlib.org/toms/index.html.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

toms446 is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version.

Related Data and Programs:

toms446_test

bernstein_polynomial, an Octave code which evaluates the Bernstein polynomials, useful for uniform approximation of functions;

chebyshev, an Octave code which computes the Chebyshev interpolant/approximant to a given function over an interval.

chebyshev_series, an Octave code which can evaluate a Chebyshev series approximating a function f(x), while efficiently computing one, two or three derivatives of the series, which approximate f'(x), f''(x), and f'''(x), by Manfred Zimmer.

divdif, an Octave code which computes interpolants by divided differences.

hermite_polynomial, an Octave code which computes the Hermite interpolant, a polynomial that matches function values and derivatives.

spline, an Octave code which can construct and evaluate spline interpolants and approximants.

test_approx, an Octave code which defines test functions for approximation and interpolation.

Author:

Original Fortran77 version by Roger Broucke; This version by John Burkardt.

Reference:

1. Roger Broucke,
   Algorithm 446: Ten Subroutines for the Manipulation of Chebyshev Series,
   Communications of the ACM,
   October 1973, Volume 16, Number 4, pages 254-256.

Source Code:

• binom.m, calculates the binomial expansion series for the (-1/M) power of a Chebyshev series.
• cheby.m, carries out the Chebyshev analysis of one or more functions.
• dfrnt.m, determines the derivative of a Chebyshev series.
• echeb.m, evaluates a Chebyshev series at a point.
• edcheb.m, evaluates the derivative of a Chebyshev series at a point.
• invert.m, computes the inverse Chebyshev series.
• mltply.m, multiplies two Chebyshev series.
• ntgrt.m, determines the integral of a Chebyshev series.
• xalfa2.m, computes a Chebyshev series raised to the (-1/M) power.
• xalfa3.m, computes a Chebyshev series raised to the (-1/M) power.