TOMS446
Ten Subroutines for the Manipulation of Chebyshev Series

TOMS446 is a C++ 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 FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

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

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

CHEBYSHEV_SERIES, a C++ 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 C++ library which computes interpolants by divided differences.

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

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

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

Author:

Original FORTRAN77 version by Roger Broucke; C++ 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.cpp, the source code.
• toms446.hpp, the include file.
• toms446.sh, commands to compile the source code.

Examples and Tests:

• toms446_prb.cpp, 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:

• BINOM: binomial expansion series for the (-1/M) power of a Chebyshev series.
• CHEBY carries out the Chebyshev analysis of one or more functions.
• DFRNT determines the derivative of a Chebyshev series.
• ECHEB evaluates a Chebyshev series at a point.
• EDCHEB evaluates the derivative of a Chebyshev series at a point.
• INVERT computes the inverse Chebyshev series.
• MLTPLY_NEW multiplies two Chebyshev series.
• MLTPLY_NEW multiplies two Chebyshev series.
• NTGRT determines the integral of a Chebyshev series.
• R8_ABS returns the absolute value of an R8.
• R8VEC_ADD adds one R8VEC to another.
• R8VEC_COPY copies an R8VEC.
• R8VEC_COPY_NEW copies an R8VEC to a "new" R8VEC.
• R8VEC_SCALE multiples an R8VEC by a scale factor.
• R8VEC_ZERO_NEW creates and zeroes an R8VEC.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• 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 C++ source codes.