# chebyshev_interp_1d

chebyshev_interp_1d, a Python 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 code. The test program needs the TEST_INTERP code.

### 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 python 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.

lagrange_interp_1d, a python 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 python code which interpolates a set of data using a piecewise constant interpolant defined by the nearest neighbor criterion.

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

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

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

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

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

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

vandermonde_interp_1d, a python 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:

The program plots a piecewise linear interpolant to the original data, and the Chebyshev interpolant.

• p01_data.png, a plot of the data and piecewise linear interpolant for problem p01;
• p01_poly.png, a plot of the polynomial interpolant for problem p01;
• p02_data.png, a plot of the data and piecewise linear interpolant for problem p02;
• p02_poly.png, a plot of the polynomial interpolant for problem p02;
• p03_data.png, a plot of the data and piecewise linear interpolant for problem p03;
• p03_poly.png, a plot of the polynomial interpolant for problem p03;
• p04_data.png, a plot of the data and piecewise linear interpolant for problem p04;
• p04_poly.png, a plot of the polynomial interpolant for problem p04;
• p05_data.png, a plot of the data and piecewise linear interpolant for problem p05;
• p05_poly.png, a plot of the polynomial interpolant for problem p05;
• p06_data.png, a plot of the data and piecewise linear interpolant for problem p06;
• p06_poly.png, a plot of the polynomial interpolant for problem p06;
• p07_data.png, a plot of the data and piecewise linear interpolant for problem p07;
• p07_poly.png, a plot of the polynomial interpolant for problem p07;
• p08_data.png, a plot of the data and piecewise linear interpolant for problem p08;
• p08_poly.png, a plot of the polynomial interpolant for problem p08;