Dimensionality Reducing Expansion of Multivariate Integration

He, Tian-Xiao

ISBN 10: 081764170X / ISBN 13: 9780817641702

Published by Birkhäuser, 2001

About this Item

Seller Inventory # 206828-n

Bibliographic Details

• Title: Dimensionality Reducing Expansion of Multivariate Integration
• Publisher: Birkhäuser
• Publication Date: 2001
• Language: English
• ISBN 10: 081764170X
• ISBN 13: 9780817641702
• Binding: Hardcover
• Condition: New

About this title

Synopsis

Multivariate integration has been a fundamental subject in mathematics, with broad connections to a number of areas: numerical analysis, approximation theory, partial differential equations, integral equations, harmonic analysis, etc. In this work the exposition focuses primarily on a powerful tool that has become especially important in our computerized age, namely, dimensionality reducing expansion (DRE). The method of DRE is a technique for changing a higher dimensional integration to a lower dimensional one with or without remainder. To date, there is no comprehensive treatment of this subject in monograph or textbook form.

Key features of this self-contained monograph include:

* fine exposition covering the history of the subject

* up-to-date new results, related to many fields of current research such as boundary element methods for solving PDEs and wavelet analysis

* presentation of DRE techniques using a broad array of examples

* good balance between theory and application

* coverage of such related topics as boundary type quadratures and asymptotic expansions of oscillatory integrals

* excellent and comprehensive bibliography and index

This work will appeal to a broad audience of students and researchers in pure and applied mathematics, statistics, and physics, and can be used in a graduate/advanced undergraduate course or as a standard reference text.