chebyshev_series, a Fortran90 code which can evaluate a Chebyshev series approximating a function f(x), while efficiently computing one, two, three or four derivatives of the series, by Manfred Zimmer.
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.
The information on this web page is distributed under the MIT license.
chebyshev_series is available in a C version and a C++ version and a Fortran77 version and a Fortran90 version and a MATLAB version and an Octave version.
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.
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.
Manfred Zimmer