Ronny Ramlau, Lothar Reichel (Hg.)


ETNA - Electronic Transactions on Numerical Analysis






ISBN 978-3-7001-8258-0
Online Edition

  Research Article
Open access


Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613.

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Austrian Academy of Sciences Press
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ETNA - Electronic Transactions on Numerical Analysis



ISBN 978-3-7001-8258-0
Online Edition



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Verlag der Österreichischen Akademie der Wissenschaften
Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2,
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doi:10.1553/etna_vol58s432



doi:10.1553/etna_vol58s432



Thema: natural
Ronny Ramlau, Lothar Reichel (Hg.)


ETNA - Electronic Transactions on Numerical Analysis






ISBN 978-3-7001-8258-0
Online Edition

  Research Article
Open access


Jilali Abouir, Brahim Benouahmane, Yassine Chakir
PDF Icon  Rational symbolic cubature rules over the first quadrant in a Cartesian plane ()
S.  432 - 449
doi:10.1553/etna_vol58s432

Open access

Verlag der Österreichischen Akademie der Wissenschaften


doi:10.1553/etna_vol58s432
Abstract:
In this paper we introduce a new symbolic Gaussian formula for theevaluation of an integral over the first quadrant in a Cartesianplane, in particular with respect to the weight function$w(x)=\exp(-x^T x-1/x^T x)$, where $x=(x_1,x_2)^T\in \mathbb{R}^2_+$. Itintegrates exactly a class of homogeneous Laurent polynomials withcoefficients in the commutative field of rational functions in twovariables. It is derived using the connection between orthogonalpolynomials, two-point Padé approximants, and Gaussian cubatures.We also discuss the connection to two-point Padé-typeapproximants in order to establish symbolic cubature formulas ofinterpolatory type. Numerical examples are presented toillustrate the different formulas developed in the paper.

Keywords:  homogeneous orthogonal polynomials, homogeneous two-point Padé, symbolic Gaussian cubature
  2023/05/02 10:16:23
Object Identifier:  0xc1aa5576 0x003e37d3
.

Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613.



Verlag der Österreichischen Akademie der Wissenschaften
Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400
https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at