Re: [eigen] Module for orth. Polynomials |

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*To*: <eigen@xxxxxxxxxxxxxxxxxxx>*Subject*: Re: [eigen] Module for orth. Polynomials*From*: "Claas H. Köhler" <claas.koehler@xxxxxx>*Date*: Mon, 25 Aug 2014 12:40:54 +0200*Organization*: Deutsches Zentrum für Luft-und Raumfahrt

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) Regards Claas 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 www.DLR.de/EOC

**Follow-Ups**:**Re: [eigen] Module for orth. Polynomials***From:*Sreekumar Thaithara Balan

**References**:**[eigen] Module for orth. Polynomials***From:*Roman Pascal Schärer

**Re: [eigen] Module for orth. Polynomials***From:*Manuel Yguel

**Re: [eigen] Module for orth. Polynomials***From:*Pavel Holoborodko

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