DIVDIF, a C++ library which creates, prints and manipulates divided difference polynomials.
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 into 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 computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
DIVDIF is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.
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