research-article

Generalized Gaussian Quadratures and Singular Value Decompositions of Integral Operators

Authors:

N. Yarvin,

V. RokhlinAuthors Info & Claims

SIAM Journal on Scientific Computing, Volume 20, Issue 2

Pages 699 - 718

https://doi.org/10.1137/S1064827596310779

Published: 01 January 1998 Publication History

Abstract

Generalized Gaussian quadratures appear to have been introduced by Markov late in the last century and have been studied in great detail as a part of modern analysis. They have not been widely used as a computational tool, in part due to an absence of effective numerical schemes for their construction. Recently, a numerical scheme for the design of such quadratures was introduced by Ma et al.; numerical results presented in their paper indicate that such quadratures dramatically reduce the computational cost of the evaluation of integrals under certain conditions. In this paper, we modify their approach, improving the stability of the scheme and extending its range of applicability. The performance of the method is illustrated with several numerical examples.

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Generalized Gaussian Quadratures and Singular Value Decompositions of Integral Operators
1. Mathematics of computing
  1. Mathematical analysis

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cover image SIAM Journal on Scientific Computing

SIAM Journal on Scientific Computing Volume 20, Issue 2

1998

387 pages

ISSN:1064-8275

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Society for Industrial and Applied Mathematics

United States

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Published: 01 January 1998

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Chen D(2023)A hybrid stochastic interpolation and compression method for kernel matricesJournal of Computational Physics10.1016/j.jcp.2023.112491494:COnline publication date: 1-Dec-2023
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