HERMITE is a MATLAB library which constructs the Hermite polynomial which interpolates function and derivative values at given points.
In other words, the user supplies n sets of data, (x(i),y(i),yp(i)), and the algorithm determines a polynomial p(x) such that, for 1 <= i <= n
p(x(i)) = y(i)
p'(x(i)) = yp(i)
Note that p(x) is a "global" polynomial, not a piecewise polynomial. Given n data points, p(x) will be a polynomial of degree 2n-1. As the value n increases, the increasing degree of the interpolating polynomial makes it liable to oscillations between the data, and eventually to severe inaccuracy even at the data points.
Generally, the interpolation problem for a large number of data points should be handled differently, for instance by piecewise polynomials.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
HERMITE is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.
BERNSTEIN_POLYNOMIAL, a MATLAB library which evaluates the Bernstein polynomials, useful for uniform approximation of functions;
CHEBYSHEV, a MATLAB library which computes the Chebyshev interpolant/approximant to a given function over an interval.
DIVDIF, a MATLAB library which computes interpolants by divided differences.
HERMITE_CUBIC, a MATLAB library which can compute the value, derivatives or integral of a Hermite cubic polynomial, or manipulate an interpolating function made up of piecewise Hermite cubic polynomials.
INTERP, a MATLAB library which can be used for parameterizing and interpolating data;
LAGRANGE_INTERP_1D, a MATLAB library which defines and evaluates the Lagrange polynomial p(x) which interpolates a set of data, so that p(x(i)) = y(i).
RBF_INTERP_1D, a MATLAB library which defines and evaluates radial basis function (RBF) interpolants to 1D data.
SHEPARD_INTERP_1D, a MATLAB library which defines and evaluates Shepard interpolants to 1D data, which are based on inverse distance weighting.
SPLINE, a MATLAB library which includes many routines to construct and evaluate spline interpolants and approximants.
TEST_INTERP_1D, a MATLAB library which defines test problems for interpolation of data y(x), depending on a 1D argument.
VANDERMONDE_INTERP_1D, a MATLAB library 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.
You can go up one level to the MATLAB source codes.