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Dimensionality Reducing Expansion of Multivariate Integration - Tian-Xiao He

Dimensionality Reducing Expansion of Multivariate Integration

By: Tian-Xiao He

Hardcover | 30 March 2001

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Multivariate integration has been a fundamental subject in mathematics, with broad connections to a number of areas: numerical integration, partial differential equations and Green's functions, harmonic analysis, numerical analysis and approximation theory. In this work the exposition focuses primarily on a powerful tool which has become especially important in our computerized age, namely, dimensionality reducing expansion (DRE). The method of dimensionally reducing expansion (DRE) is a technique for changing a higher dimensional integration to a lower dimensional one with or without remainder. Key features of this monograph include: fine exposition covering the history of the subject; up-to-date new results; presentation of dimensionality reducing expansion (DRE) technique using broad array of examples, illustrations and problem sets; balance between theory and applications; coverage of such related topics as boundary type quadratures and asymptotic expansions of oscillatory integrals; bibliography and index; and broad appeal to mathematicians, statisticians and physicists.

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