chebyshev_series


chebyshev_series, a FORTRAN90 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.

Note that this code does not compute a Chebyshev series; it assumes that the series has already been computed, and offers an efficient means of evaluating the series and its derivatives simultaneously.

Licensing:

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

Languages:

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

Related Data and Programs:

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

CHEBYSHEV_INTERP_1D, a FORTRAN90 code which determines the combination of Chebyshev polynomials which interpolates a set of data, so that p(x(i)) = y(i).

CHEBYSHEV_POLYNOMIAL, a FORTRAN90 code which considers the Chebyshev polynomials T(i,x), U(i,x), V(i,x) and W(i,x). Functions are provided to evaluate the polynomials, determine their zeros, produce their polynomial coefficients, produce related quadrature rules, project other functions onto these polynomial bases, and integrate double and triple products of the polynomials.

chebyshev_series_test

CLAUSEN, a FORTRAN90 code which evaluates a Chebyshev interpolant to the Clausen function Cl2(x).

FN, a FORTRAN90 code which approximates elementary and special functions using Chebyshev polynomials; functions include Airy, Bessel I, J, K and Y, beta, confluent hypergeometric, error, gamma, log gamma, Pochhammer, Spence; integrals include hyperbolic cosine, cosine, Dawson, exponential, logarithmic, hyperbolic sine, sine; by Wayne Fullerton.

POLPAK, a FORTRAN90 code which evaluates a variety of mathematical functions, including Chebyshev, Gegenbauer, Hermite, Jacobi, Laguerre, Legendre polynomials, and the Collatz sequence.

TOMS446, a FORTRAN90 code which manipulates Chebyshev series for interpolation and approximation; this is ACM TOMS algorithm 446, by Roger Broucke.

Author:

Manfred Zimmer

Reference:

  1. Charles Clenshaw,
    Mathematical Tables, Volume 5,
    Chebyshev series for mathematical functions,
    London, 1962.
  2. Gerhard Maess,
    Vorlesungen ueber Numerische Mathematik II, Analysis,
    Berlin, Akademie_Verlag, 1984-1988,
    ISBN: 978-3764318840,
    LC: QA297.M325.  
  3. Francis Smith,
    An algorithm for summing orthogonal polynomial series and their derivatives with applications to curve-fitting and interpolation,
    Mathematics of Computation,
    Volume 19, Number 89, 1965, pages 33-36.

Source Code:


Last revised on 08 June 2020.