|Re: [eigen] Module for orth. Polynomials|
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As a side note:
Some time ago I also implemented a Gauss integration with Legendre Polynomials and found that the
Goloub-Welsh method is not very effective for the calculaton of the roots. I implemented another
method (first guess based on heuristic formula followed by Newton like iteration), which usually
outperformed the Goloub method. If this is of interest, I could submit the code, which is template
based and should allow for arbitrary precision (I tested up to Quad precision only, though)
On 25/08/14 10:38, Pavel Holoborodko wrote:
> This module would be of high value indeed.
> Especially in combination with multi-precision support.
> Then Eigen would have full spectrum of classic numerical integration methods (and in arbitrary
> (As far as I know, adaptive Guass-Kronrod is being developed as another module for Eigen as well)
> On Mon, Aug 25, 2014 at 5:19 PM, Manuel Yguel <manuel.yguel@xxxxxxxxx
> <mailto:manuel.yguel@xxxxxxxxx>> wrote:
> Great !
> I think it is a nice thing to have, I am interested to take a look at it.
> Dr. Ing. Manuel Yguel
> Porteur du projet StraTagGem
> 36, rue de l'Université
> 67000, Strasbourg.
> Tel: +33 9 73 52 86 75 <tel:%2B33%20%209%2073%2052%2086%2075>
> Mobile: +33 6 59 59 17 30 <tel:%2B33%20%206%2059%2059%2017%2030>
> On 08/25/2014 10:16 AM, Roman Pascal Schärer wrote:
> 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.
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