TOMS446
Ten Subroutines for the Manipulation of Chebyshev Series

TOMS446 is a FORTRAN90 library which implements ACM TOMS algorithm 446, for the manipulation of Chebyshev series, by Roger Broucke.

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:

TOMS446 is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

BERNSTEIN_POLYNOMIAL, a FORTRAN90 library which evaluates the Bernstein polynomials, useful for uniform approximation of functions;

CHEBYSHEV, a FORTRAN90 library which computes the Chebyshev interpolant/approximant to a given function over an interval.

CHEBYSHEV_SERIES, a FORTRAN90 library 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 FORTRAN90 library which computes interpolants by divided differences.

HERMITE, a FORTRAN90 library which computes the Hermite interpolant, a polynomial that matches function values and derivatives.

PPPACK, a FORTRAN90 library which computes piecewise polynomial functions, including cubic splines.

SPLINE, a FORTRAN90 library which can construct and evaluate spline interpolants and approximants.

TEST_APPROX, a FORTRAN90 library which defines test functions for approximation and interpolation.

Author:

Original FORTRAN77 version by Roger Broucke; FORTRAN90 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:

• toms446.f90, the source code.

Examples and Tests:

• toms446_test.f90, a sample calling program.
• toms446_test.txt, the output from a run of the sample program.

List of Routines:

• CHEBY carries out the Chebyshev analysis of one or more functions.
• MLTPLY multiplies two Chebyshev series.
• ECHEB evaluates a Chebyshev series at a point.
• EDCHEB evaluates the derivative of a Chebyshev series at a point.
• DFRNT determines the derivative of a Chebyshev series.
• NTGRT determines the integral of a Chebyshev series.
• INVERT computes the inverse Chebyshev series.
• BINOM calculates the binomial expansion series for the (-1/M) power of a Chebyshev series.
• XALFA2 computes a Chebyshev series raised to the (-1/M) power.
• XALFA3 computes a Chebyshev series raised to the (-1/M) power.

You can go up one level to the FORTRAN90 source codes.