HERMITE is a FORTRAN90 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 FORTRAN90 version and a MATLAB version.
BERNSTEIN_POLYNOMIAL, a FORTRAN90 library which evaluates the Bernstein polynomials, useful for uniform approximation of functions;
CHEBYSHEV, a FORTRAN90 library which computes the Chebyshev interpolant/approximant to a given function over an interval.
DIVDIF, a FORTRAN90 library which computes interpolants by divided differences.
HERMITE_CUBIC, a FORTRAN90 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 FORTRAN90 library which can compute interpolants to data.
LAGRANGE_INTERP_1D, a FORTRAN90 library which defines and evaluates the Lagrange polynomial p(x) which interpolates a set of data, so that p(x(i)) = y(i).
PPPACK, a FORTRAN90 library which computes piecewise polynomial functions, including cubic splines.
RBF_INTERP, a FORTRAN90 library which defines and evaluates radial basis interpolants to multidimensional data.
SPLINE, a FORTRAN90 library which includes many routines to construct and evaluate spline interpolants and approximants.
TEST_INTERP, a FORTRAN90 library which defines a number of test problems for interpolation.
TOMS446,
a FORTRAN90 library which
manipulates Chebyshev series for interpolation and approximation;
this is a version of ACM TOMS algorithm 446,
by Roger Broucke.
You can go up one level to the FORTRAN90 source codes.