Efficient algorithms for multivariate and ∞-Variate integration with exponential weight

L. Plaskota; G. W. Wasilkowski

doi:10.1007/s11075-013-9798-4

Efficient algorithms for multivariate and ∞-Variate integration with exponential weight

L. Plaskota, G. W. Wasilkowski

Computer Science

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

Using the Multivariate Decomposition Method (MDM), we develop an efficient algorithm for approximating the8-variate integralfor a class of functions f that are once differentiable with respect to each variable.MDM requires efficient algorithms for d-variate versions of the problem. Such algorithms are provided by Smolyaks construction which is based on efficient algorithms for the univariate integrationDetailed analysis and development of (nearly) optimal quadratures for I (f) is the main contribution of the current paper.

Original language	English
Pages (from-to)	385-403
Number of pages	19
Journal	Numerical Algorithms
Volume	67
Issue number	2
DOIs	https://doi.org/10.1007/s11075-013-9798-4
State	Published - Sep 25 2014

Bibliographical note

Publisher Copyright:
© 2013, Springer Science+BusinessMedia New York.

Keywords

Multivariate integration
Weighted integrals
Weighted trapezoid rules
∞-Variate functions

ASJC Scopus subject areas

Applied Mathematics

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10.1007/s11075-013-9798-4

Cite this

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N2 - Using the Multivariate Decomposition Method (MDM), we develop an efficient algorithm for approximating the8-variate integralfor a class of functions f that are once differentiable with respect to each variable.MDM requires efficient algorithms for d-variate versions of the problem. Such algorithms are provided by Smolyaks construction which is based on efficient algorithms for the univariate integrationDetailed analysis and development of (nearly) optimal quadratures for I (f) is the main contribution of the current paper.

AB - Using the Multivariate Decomposition Method (MDM), we develop an efficient algorithm for approximating the8-variate integralfor a class of functions f that are once differentiable with respect to each variable.MDM requires efficient algorithms for d-variate versions of the problem. Such algorithms are provided by Smolyaks construction which is based on efficient algorithms for the univariate integrationDetailed analysis and development of (nearly) optimal quadratures for I (f) is the main contribution of the current paper.

KW - Multivariate integration

KW - Weighted integrals

KW - Weighted trapezoid rules

KW - ∞-Variate functions

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Efficient algorithms for multivariate and ∞-Variate integration with exponential weight

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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