# 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.

### 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.

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:

• chebyshev_coef_1d.m, determines the coefficients of the Chebyshev interpolant for a set of data.
• chebyshev_interp_1d.m, determines the coefficients of the Chebyshev interpolant for a set of data and evaluates the interpolant.
• chebyshev_value_1d.m, evaluates a Chebyshev interpolant, given its coefficients.