TOMS446
Ten Subroutines for the Manipulation of Chebyshev Series

TOMS446 is a FORTRAN77 library 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: http://www.acm.org/pubs/calgo or NETLIB: http://www.netlib.org/toms/index.html.

Languages:

TOMS446 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_POLYNOMIAL, a FORTRAN77 library which evaluates the Bernstein polynomials, useful for uniform approximation of functions;

CHEBYSHEV_SERIES, a FORTRAN77 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 FORTRAN77 library which computes interpolants by divided differences.

Author:

Original FORTRAN77 version by Roger Broucke; This FORTRAN77 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.f, the source code.
• toms446.sh, commands to compile the source code.

Examples and Tests:

• toms446_prb.f, a sample calling program.
• toms446_prb.sh, commands to compile and run the sample program.
• toms446_prb_output.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 FORTRAN77 source codes.