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Dimensionality Reducing Expansion of Multivariate Integration - Tian-Xiao He

Dimensionality Reducing Expansion of Multivariate Integration

(Autor)

Buch | Softcover
227 Seiten
2011 | Softcover reprint of the original 1st ed. 2001
Springer-Verlag New York Inc.
978-1-4612-7414-8 (ISBN)
CHF 74,85 inkl. MwSt
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.

1 Dimensionality Reducing Expansion of Multivariate Integration.- 1.1 Darboux formulas and their special forms.- 1.2 Generalized integration by parts rule.- 1.3 DREs with algebraic precision.- 1.4 Minimum estimation of remainders in DREs with algebraic precision.- 2 Boundary Type Quadrature Formulas with Algebraic Precision.- 2.1 Construction of BTQFs using DREs.- 2.2 BTQFs with homogeneous precision.- 2.3 Numerical integration associated with wavelet functions.- 2.4 Some applications of DREs and BTQFs.- 2.5 BTQFs over axially symmetric regions.- 3 The Integration and DREs of Rapidly Oscillating Functions.- 3.1 DREs for approximating a double integral.- 3.2 Basic lemma.- 3.3 DREs with large parameters.- 3.4 Basic expansion theorem for integrals with large parameters.- 3.5 Asymptotic expansion formulas for oscillatory integrals with singular factors.- 4 Numerical Quadrature Formulas Associated with the Integration of Rapidly Oscillating Functions.- 4.1 Numerical quadrature formulas of double integrals.- 4.2 Numerical integration of oscillatory integrals.- 4.3 Numerical quadrature of strongly oscillatory integrals with compound precision.- 4.4 Fast numerical computations of oscillatory integrals.- 4.5 DRE construction and numerical integration using measure theory.- 4.6 Error analysis of numerical integration.- 5 DREs Over Complex Domains.- 5.1 DREs of the double integrals of analytic functions.- 5.2 Construction of quadrature formulas using DREs.- 5.3 Integral regions suitable for DREs.- 5.4 Additional topics.- 6 Exact DREs Associated With Differential Equations.- 6.1 DREs and ordinary differential equations.- 6.2 DREs and partial differential equations.- 6.3 Applications of DREs in the construction of BTQFs.- 6.4 Applications of DREs in the boundary element method.

Zusatzinfo XI, 227 p.
Verlagsort New York, NY
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Mathematik Allgemeines / Lexika
Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Angewandte Mathematik
Mathematik / Informatik Mathematik Wahrscheinlichkeit / Kombinatorik
Wirtschaft Volkswirtschaftslehre Ökonometrie
ISBN-10 1-4612-7414-1 / 1461274141
ISBN-13 978-1-4612-7414-8 / 9781461274148
Zustand Neuware
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