test_interp_fun

test_interp_fun, a Fortran77 code which defines functions whose sampled data can be used in testing interpolation algorithms.

The related packages TEST_INTERP and TEST_APPROX provide discrete data sets of (x,y) pairs. However, when the convergence rate of an interpolation process is of interest, it is important to be able to sample an underlying but "unknown" function at an increasing number of points. This library provides a few functions which are known to cause problems for certain kinds of interpolation schemes.

The problems available include:

1. Runge example, f(x) = 1 / ( x * x + 1 ), [-5,5], p01_plot.png;
2. Bernstein example, f(x) = abs ( x ), [-1,1], p02_plot.png;
3. The Step function, p03_plot.png;
4. The Doppler function, p04_plot.png;
5. The Rabbit Ears function, p05_plot.png;

Licensing:

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

Languages:

test_interp_fun is available in a MATLAB version and. an Octave version.

Related Data and Programs:

test_interp_fun_test

chebyshev, a Fortran77 library which computes the Chebyshev interpolant/approximant to a given function over an interval.

divdif, a Fortran77 library which includes many routines to construct and evaluate divided difference interpolants.

PPPACK, a Fortran77 library which implements Carl de Boor's piecewise polynomial functions, including, particularly, cubic splines.

RBF_INTERP, a Fortran77 library which defines and evaluates radial basis interpolants to multidimensional data.

SPLINE, a Fortran77 library which includes many routines to construct and evaluate spline interpolants and approximants.

TEST_APPROX, a Fortran77 library which defines test problems for approximation, provided as a set of (x,y) data.

TEST_INTERP, a Fortran77 library which defines a number of test problems for interpolation, provided as a set of (x,y) data.

TOMS446, a Fortran77 library which manipulates Chebyshev series for interpolation and approximation;
this is a version of ACM TOMS algorithm 446, by Roger Broucke.

Reference:

1. Samuel Conte, Carl deBoor,
   Elementary Numerical Analysis,
   Second Edition,
   McGraw Hill, 1972,
   ISBN: 07-012446-4,
   LC: QA297.C65.
2. Carl deBoor,
   A Practical Guide to Splines,
   Springer, 2001,
   ISBN: 0387953663,
   LC: QA1.A647.v27.

Source Code:

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