Re: [eigen] Module for orth. Polynomials |

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*To*: eigen@xxxxxxxxxxxxxxxxxxx*Subject*: Re: [eigen] Module for orth. Polynomials*From*: Manuel Yguel <manuel.yguel@xxxxxxxxx>*Date*: Mon, 25 Aug 2014 15:05:38 +0200*Dkim-signature*: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20120113; h=message-id:date:from:user-agent:mime-version:to:subject:references :in-reply-to:content-type:content-transfer-encoding; bh=1QCS2kWMfiEyALU9VQauDsWe3Kgn14R7ELIWln2SvUc=; b=I0GcNVoIz3zem1PojXezoiomwsIIXkXd7XzQJELfbGOArpbma6IxNshM/VCT8k3ko/ BV+vQFogBfqcLrQqk/qyf8cVhXhIS/Udt9rC0eZ7kDFBh32hfzkNHpFe0FJPjm2PIlFa eixjaagAJXkm31mifkhTpMZivO/eU7ce9vSL56FyeVnKwBgvNnjqxLochlueBmCZFTw9 CNPpKOQZp4nCpglTsv7fXj4vkf2ulwb6W8vG9GgxVQlHrH7a0rStFDzauox9Vak4M6zC NOOTWcYpQg8Z0rE4WHNM4D7uiPNtyWh4iVO+Rz+yB6e3jdCOwMHu327oPAfhitHVM5wq uBPQ==

Dr. Ing. Manuel Yguel Porteur du projet StraTagGem 36, rue de l'Université 67000, Strasbourg. FRANCE Tel: +33 9 73 52 86 75 Mobile: +33 6 59 59 17 30 On 08/25/2014 10:59 AM, Christoph Hertzberg wrote:

Definitely sounds interesting.Independent of that, the polynomial module could need some (verybasic) functionality, like polynomial multiplication/division and evenaddition (of polynomials with different degree):

I definitely agree and it is on my todo list since a long time.

http://eigen.tuxfamily.org/bz/show_bug.cgi?id=700 Having that, could simplify writing unit tests. Christoph On 25.08.2014 10:16, Roman Pascal Schärer wrote:Dear Eigen developers and users,we developed a small C++ package for the computation of orthogonalpolynomials (OPQ++) as an unsupported module inside Eigen for our ownneeds.The main goal of this package is to provide methods to compute anorthogonal set of polynomials for a given weight function. This hasbeen realised with the modified Chebyshev algorithm, which computesthe recurrence coefficients of the polynomials. This algorithm makesuse of the moments of the weight function, which in general need tobe computed using some numerical integration method. For now weprovide our own implementations of quadrature formulas (e.q. Gaussianquadratures). With the obtained recurrence coefficients the nodes andweights of a Gaussian quadrature formula for the weight function canbe 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 madepublic. Since it is a rather small module, it could e.g. also beintegrated in the “Polynomials Module”.If such interest exists, we would be open for suggestions regardingthe API and the implementation of more features such asmulti-precision floating point number support etc.Best, Roman

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

**Re: [eigen] Module for orth. Polynomials***From:*Christoph Hertzberg

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