toms446

toms446, a MATLAB 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 computer code and data files described and made available on this web page are 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.

Related Data and Programs:

toms446_test

bernstein_polynomial, a MATLAB code which evaluates the Bernstein polynomials, useful for uniform approximation of functions;

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

chebyshev_series, a MATLAB 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, a MATLAB code which computes interpolants by divided differences.

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

spline, a MATLAB code which can construct and evaluate spline interpolants and approximants.

test_approx, a MATLAB code which defines test functions for approximation and interpolation.

Author:

Original FORTRAN77 version by Roger Broucke; Matlab 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.