Re: [eigen] Module for orth. Polynomials

[ Thread Index | Date Index | More Archives ]

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
> precision!).
> (As far as I know, adaptive Guass-Kronrod is being developed as another module for Eigen as well)
> Pavel. 
> 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.
>     FRANCE
>     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.
>         Best,
>         Roman

Deutsches Zentrum für Luft- und Raumfahrt e.V. (DLR)
Institut für Methodik der Fernerkundung | Experimentelle Verfahren | Münchener Str 20| 82234 Weßling

Dr. Claas H. Köhler
Telefon 08153 28-1274 | Telefax 08153 28-1337 | claas.koehler@xxxxxx

Mail converted by MHonArc 2.6.19+