[eigen] Module for orth. Polynomials

[Roman Pascal Schärer <romanus@xxxxxxxxxx>]

Dear Eigen developers and users,

we developed a small C++ package  for the computation of orthogonal polynomials (OPQ++) as an unsupported module inside Eigen for our own needs.

The main goal of this package is to provide methods to compute an orthogonal set of polynomials for a given weight function. This has been realised with the modified Chebyshev algorithm, which computes the recurrence coefficients of the polynomials. This algorithm makes use of the moments of the weight function, which in general need to be computed using some numerical integration method. For now we provide our own implementations of quadrature formulas (e.q. Gaussian quadratures). With the obtained recurrence coefficients the nodes and weights of a Gaussian quadrature formula for the weight function can be easily computed using e.g. the Golub-Welsch algorithm.

Since this package could be easily integrated in the Eigen library, I’d like to ask if there is interest for such a module to be made public. Since it is a rather small module, it could e.g. also be integrated in the “Polynomials Module”.

If such interest exists, we would be open for suggestions regarding the API and the implementation of more features such as multi-precision floating point number support etc.

Best,
Roman