hermite_interpolant, a Fortran90 code 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 information on this web page is distributed under the MIT license.
hermite_interpolant is available in a C version and a C++ version and a Fortran77 version and a Fortran90 version and a MATLAB version and an Octave version.
bernstein_polynomial, a Fortran90 code which evaluates the Bernstein polynomials, useful for uniform approximation of functions;
chebyshev, a Fortran90 code which computes the Chebyshev interpolant/approximant to a given function over an interval.
divdif, a Fortran90 code which computes interpolants by divided differences.
hermite_cubic, a Fortran90 code 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 code which can compute interpolants to data.
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).
pppack, a Fortran90 code which computes piecewise polynomial functions, including cubic splines.
rbf_interp, a Fortran90 code which defines and evaluates radial basis interpolants to multidimensional data.
spline, a Fortran90 code which includes many routines to construct and evaluate spline interpolants and approximants.
test_interp, a Fortran90 code which defines a number of test problems for interpolation.
toms446,
a Fortran90 code which
manipulates Chebyshev series for interpolation and approximation;
this is a version of ACM TOMS algorithm 446,
by Roger Broucke.