CHEBYSHEV_INTERP_1D
Chebyshev Polynomial Interpolation in 1D

CHEBYSHEV_INTERP_1D is a FORTRAN77 library 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 QR_SOLVE and R8LIB libraries. 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 GNU LGPL license.

Languages:

CHEBYSHEV_INTERP_1D 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:

BARYCENTRIC_INTERP_1D, a FORTRAN77 library 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 FORTRAN77 library which computes the Chebyshev interpolant/approximant to a given function over an interval.

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 uses divided differences to compute the polynomial interpolant to a given set of data.

HERMITE, a FORTRAN77 library which computes the Hermite interpolant, a polynomial that matches function values and derivatives.

LAGRANGE_INTERP_1D, a FORTRAN77 library 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 FORTRAN77 library which interpolates a set of data using a piecewise constant interpolant defined by the nearest neighbor criterion.

PWL_INTERP_1D, a FORTRAN77 library which interpolates a set of data using a piecewise linear interpolant.

QR_SOLVE, a FORTRAN77 library which computes the least squares solution of a linear system A*x=b.

R8LIB, a FORTRAN77 library which contains many utility routines using double precision real (R8) arithmetic.

RBF_INTERP_1D, a FORTRAN77 library which defines and evaluates radial basis function (RBF) interpolants to 1D data.

SHEPARD_INTERP_1D, a FORTRAN77 library which defines and evaluates Shepard interpolants to 1D data, based on inverse distance weighting.

SPLINE, a FORTRAN77 library which constructs and evaluates spline interpolants and approximants.

TEST_INTERP, a FORTRAN77 library which defines a number of test problems for interpolation, provided as a set of (x,y) data.

TEST_INTERP_1D, a FORTRAN77 library which defines test problems for interpolation of data y(x), depending on a 2D argument.

VANDERMONDE_INTERP_1D, a FORTRAN77 library which finds a polynomial interpolant to data y(x) of a 1D argument, 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:

• chebyshev_interp_1d.f, the source code.
• chebyshev_interp_1d.sh, BASH commands to compile the source code.

Examples and Tests:

• chebyshev_interp_1d_prb.f, a sample calling program.
• chebyshev_interp_1d_prb.sh, BASH commands to compile and run the sample program.
• chebyshev_interp_1d_prb_output.txt, the output file.

List of Routines:

• CHEBYSHEV_COEF_1D determines the Chebyshev interpolant coefficients.
• CHEBYSHEV_INTERP_1D determines and evaluates the Chebyshev interpolant.
• CHEBYSHEV_VALUE_1D evaluates a Chebyshev interpolant, given its coefficients.

You can go up one level to the FORTRAN77 source codes.