hermite_interpolant, a C++ 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_interpolant is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.
BERNSTEIN_POLYNOMIAL, a C++ library which evaluates the Bernstein polynomials, useful for uniform approximation of functions;
CHEBYSHEV, a C++ library which computes the Chebyshev interpolant/approximant to a given function over an interval.
DIVDIF, a C++ library which computes interpolants by divided differences.
HERMITE_CUBIC, a C++ 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.
RBF_INTERP, a C++ library which defines and evaluates radial basis function (RBF) interpolants to multidimensional data.
SPLINE, a C++ library which includes many routines to construct and evaluate spline interpolants and approximants.
TEST_APPROX, a C++ library which defines test problems for approximation, provided as a set of (x,y) data.
TEST_INTERP_1D, a C++ library which defines test problems for interpolation of data y(x), depending on a 1D argument.