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商品詳細
Dimensionality Reducing Expansion of Multivariate Integration. Softcover reprint of the original 1st ed. 2001.
・ISBN 978-1-4612-7414-8 paper EUR 49.99
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| 著者・編者 | He, Tian-Xiao, |
|---|---|
| 出版社 | (Springer-Verlag New York Inc., US) |
| 出版年月 | 2011 |
| ページ数 | 227 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-17383＞ |
解説
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.