divdif, a Fortran90 code which creates, prints and manipulates divided difference polynomials from a table of values (x,f(x)). The code can compute the coefficients of the Newton and power sum forms of the interpolating polynomial. It can compute the derivative or antiderivate polynomial. It can compute the form of the Lagrange basis polynomials. It can compute the points and weights for Newton Cotes quadrature rules. It can compute the weights for a Lagrange interpolation scheme.
Divided difference polynomials are a systematic method of computing polynomial approximations to scattered data. The representations are compact, and may easily be updated with new data, rebased at zero, or analyzed to produce the standard form polynomial, integral or derivative polynomials.
Other routines are available to convert the divided difference representation to standard polynomial format. This is a natural way to determine the coefficients of the polynomial that interpolates a given set of data, for instance.
One surprisingly simple but useful routine is available to take a set of roots and compute the divided difference or standard form polynomial that passes through those roots.
Finally, the Newton-Cotes quadrature formulas can be derived using divided difference methods, so a few routines are given which can compute the weights and abscissas of open or closed rules for an arbitrary number of nodes.
The information on this web page is distributed under the MIT license.
divdif 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 and a Python 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.
differ, a Fortran90 code which determines the finite difference coefficients necessary in order to combine function values at known locations to compute an approximation of given accuracy to a derivative of a given order.
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).
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 can construct and evaluate spline interpolants and approximants.
test_approx, a Fortran90 code which defines test functions for approximation and 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.
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.