Ramón Orive,
Juan C. Santos-León,
Miodrag M. Spalević
S. 426 - 438
doi:
10.1553/etna_vol53s426
Verlag der Österreichischen Akademie der Wissenschaften
doi:
10.1553/etna_vol53s426
Abstract:
In this paper we review some of the main known facts about cubature rules to approximate integrals overdomains in $\mathbb{R}^n$, in particular with respect to the Gaussian weight $\displaystyle w(\mathbf{x}) = e^{-\mathbf{x}^T\,\mathbf{x}},$where $\mathbf{x} = (x_1,\ldots,x_n)\in \mathbb{R}^n.$ Some new rules are also presented. Taking into account the well-knownissue of the “curse of dimensionality”, our aim is at providing rules with a certain degree of algebraic precision and a reasonably small number of nodes as well as an acceptable stability. We think that the methods used to construct these new rules are of further applicability in the field of cubature formulas. The efficiency of new and old rules are compared by means of several numerical experiments.
cubature formulas, Gaussian weight
Published Online:
2020/05/27 11:48:11
Object Identifier:
0xc1aa5576 0x003b8938
Rights:All rights reserved.For questions regarding copyright and copies please contact us by email.
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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