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The Theory of Cubature Formulas : MATHEMATICS AND ITS APPLICATIONS (KLUWER ) - S.L. Sobolev

The Theory of Cubature Formulas


Hardcover Published: 30th June 1997
ISBN: 9780792346319
Number Of Pages: 418

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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.

Foreword to the English Translation
From the Preface to "Introduction to the Theory of Cubature Formulas"
Problems and Results of the Theory of Cubature Formulasp. 1
Cubature Formulas of Finite Orderp. 43
Formulas with Regular Boundary Layer for Rational Polyhedrap. 74
The Rate of Convergence of Cubature Formulasp. 93
Cubature Formulas with Regular Boundary Layerp. 131
Universal Asymptotic Optimalityp. 173
Cubature Formulas of Infinite Orderp. 221
Functions of a Discrete Variablep. 292
Optimal Formulasp. 331
Referencesp. 389
Notation Indexp. 411
Subject Indexp. 413
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792346319
ISBN-10: 0792346319
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 418
Published: 30th June 1997
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.5 x 15.88  x 3.18
Weight (kg): 0.84