chebyshev_interp_1d


chebyshev_interp_1d, a MATLAB code which determines the combination of Chebyshev polynomials which interpolates a set of data, so that p(x(i)) = y(i).

CHEBYSHEV_INTERP_1D needs the R8LIB library. The test program needs the TEST_INTERP library.

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

Languages:

chebyshev_interp_1d is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

barycentric_interp_1d, a MATLAB code which defines and evaluates the barycentric lagrange polynomial p(x) which interpolates a set of data, so that p(x(i)) = y(i). the barycentric approach means that very high degree polynomials can safely be used.

chebyshev, a MATLAB code which computes the chebyshev interpolant/approximant to a given function over an interval.

chevyshev_interp_1d_test

chebyshev_series, a MATLAB 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.

clausen, a MATLAB code which evaluates a chebyshev approximant to the clausen function cl2(x).

divdif, a MATLAB code which uses divided differences to compute the polynomial interpolant to a given set of data.

hermite_polynomial, a MATLAB code which computes the hermite interpolant, a polynomial that matches function values and derivatives.

lagrange_interp_1d, a MATLAB code which defines and evaluates the lagrange polynomial p(x) which interpolates a set of data, so that p(x(i)) = y(i).

nearest_interp_1d, a MATLAB code which interpolates a set of data using a piecewise constant interpolant defined by the nearest neighbor criterion.

newton_interp_1d, a MATLAB code which finds a polynomial interpolant to data using newton divided differences.

pwl_interp_1d, a MATLAB code which interpolates a set of data using a piecewise linear interpolant.

r8lib, a MATLAB code which contains many utility routines using double precision real (r8) arithmetic.

rbf_interp_1d, a MATLAB code which defines and evaluates radial basis function (rbf) interpolants to 1d data.

shepard_interp_1d, a MATLAB code which defines and evaluates shepard interpolants to 1d data, which are based on inverse distance weighting.

spline, a MATLAB code which constructs and evaluates spline interpolants and approximants.

test_interp, a MATLAB code which defines a number of test problems for interpolation, provided as a set of (x,y) data.

test_interp_1d, a MATLAB code which defines test problems for interpolation of data y(x), depending on a 2d argument.

vandermonde_interp_1d, a MATLAB code which finds a polynomial interpolant to a function of 1d data by setting up and solving a linear system for the polynomial coefficients, involving the vandermonde matrix.

Reference:

  1. Kendall Atkinson,
    An Introduction to Numerical Analysis,
    Prentice Hall, 1989,
    ISBN: 0471624896,
    LC: QA297.A94.1989.
  2. Philip Davis,
    Interpolation and Approximation,
    Dover, 1975,
    ISBN: 0-486-62495-1,
    LC: QA221.D33
  3. David Kahaner, Cleve Moler, Steven Nash,
    Numerical Methods and Software,
    Prentice Hall, 1989,
    ISBN: 0-13-627258-4,
    LC: TA345.K34.

Source Code:


Last modified on 22 December 2018.