TOMS446
Ten Subroutines for the Manipulation of Chebyshev Series

TOMS446 is a MATLAB library which implements ACM TOMS algorithm 446, for the manipulation of Chebyshev series.

While the text of many ACM TOMS algorithms is available online through ACM: http://www.acm.org/pubs/calgo or NETLIB: http://www.netlib.org/toms/index.html, most of the early algorithms are not available. This is one of them. I typed it in.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

TOMS466 is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

BERNSTEIN, a MATLAB library which evaluates the Bernstein polynomials, useful for uniform approximation of functions;

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

DIVDIF, a MATLAB library which computes interpolants by divided differences.

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

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

TEST_APPROX, a MATLAB library which defines test functions for approximation and interpolation.

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.

Examples and Tests:

• toms446_test.m, calls all tests.
• toms446_test01.m, tests CHEBY, which computes Chebyshev series.
• toms446_test02.m, tests MULTPLY, which multiplies two Chebyshev series.
• toms446_test03.m, tests ECHEB, which evaluates a Chebyshev series.
• toms446_test04.m, tests EDCHEB, which evaluates the derivative of a Chebyshev series.
• toms446_test05.m, tests DFRNT, which computes the Chebyshev series of a derivative.
• toms446_test06.m, tests NTGRT, which computes the Chebyshev series of an indefinite integral.
• toms446_test_output.txt, the output from a run of the sample program.

You can go up one level to the MATLAB source codes.