S L Sobolev

(Author)

The Theory of Cubature FormulasPaperback, 4 February 2011

The Theory of Cubature Formulas
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Part of Series
Mathematics and Its Applications
Part of Series
Mathematics and Its Applications (Closed)
Part of Series
Mathematics and Its Applications Mathematics and Its Applica
Print Length
418 pages
Language
English
Publisher
Springer
Date Published
4 Feb 2011
ISBN-10
9048148758
ISBN-13
9789048148752

Description

This volume considers various methods for constructing cubature and quadrature formulas of arbitrary degree. These formulas are intended to approximate the calculation of multiple and conventional integrals over a bounded domain of integration. The latter is assumed to have a piecewise-smooth boundary and to be arbitrary in other aspects. Particular emphasis is placed on invariant cubature formulas and those for a cube, a simplex, and other polyhedra. Here, the techniques of functional analysis and partial differential equations are applied to the classical problem of numerical integration, to establish many important and deep analytical properties of cubature formulas. The prerequisites of the theory of many-dimensional discrete function spaces and the theory of finite differences are concisely presented. Special attention is paid to constructing and studying the optimal cubature formulas in Sobolev spaces. As an asymptotically optimal sequence of cubature formulas, a many-dimensional abstraction of the Gregory quadrature is indicated.
Audience: This book is intended for researchers having a basic knowledge of functional analysis who are interested in the applications of modern theoretical methods to numerical mathematics.

Product Details

Authors:
S L SobolevVladimir L Vaskevich
Book Format:
Paperback
Country of Origin:
NL
Date Published:
4 February 2011
Dimensions:
23.39 x 15.6 x 2.29 cm
ISBN-10:
9048148758
ISBN-13:
9789048148752
Language:
English
Location:
Dordrecht
Pages:
418
Publisher:
Weight:
612.35 gm

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