# newton_interp_1d

newton_interp_1d, a FORTRAN90 code which finds a polynomial interpolant to data using Newton divided differences.

### Languages:

newton_interp_1d is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

### Related Data and Programs:

barycentric_interp_1d, a FORTRAN90 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_interp_1d, a FORTRAN90 code which determines the combination of Chebyshev polynomials which interpolates a set of data, so that p(x(i)) = y(i).

divdif, a FORTRAN90 code which uses divided differences to compute the polynomial interpolant to a given set of data.

hermite_interpolant, a FORTRAN90 code which computes the Hermite interpolant, a polynomial that matches function values and derivatives.

lagrange_interp_1d, a FORTRAN90 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 FORTRAN90 code which interpolates a set of data using a piecewise constant interpolant defined by the nearest neighbor criterion.

pwl_interp_1d, a FORTRAN90 code which interpolates a set of data using a piecewise linear interpolant.

rbf_interp_1d, a FORTRAN90 code which defines and evaluates radial basis function (RBF) interpolants to 1D data.

shepard_interp_1d, a FORTRAN90 code which defines and evaluates Shepard interpolants to 1D data, which are based on inverse distance weighting.

spline, a FORTRAN90 code which constructs and evaluates spline interpolants and approximants.

test_interp_1d, a FORTRAN90 code which defines test problems for interpolation of data y(x), depending on a 2D argument.

vandermonde_interp_1d, a FORTRAN90 code 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.