Dimensionality reducing expansion of multivariate integration /

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...

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Bibliographic Details
Main Author:	He, Tian-Xiao, 1952-
Corporate Author:	SpringerLink (Online service)
Format:	eBook
Language:	English
Published:	Boston : Birkhäuser, [2001]
Subjects:	Numerical integration. Gaussian quadrature formulas. Green's functions. Numerische Integration. Funktion (Mathematik) Mehrere Variable. Electronic books.
Online Access:	Connect to the full text of this electronic book

Table of Contents:

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.