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The Theory of Cubature Formulas / Edition 1
     

The Theory of Cubature Formulas / Edition 1

by S.L. Sobolev, Vladimir Vaskevich
 

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ISBN-10: 9048148758

ISBN-13: 9789048148752

Pub. Date: 02/03/2011

Publisher: Springer Netherlands

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

Overview

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

ISBN-13:
9789048148752
Publisher:
Springer Netherlands
Publication date:
02/03/2011
Series:
Mathematics and Its Applications (closed) Series , #415
Edition description:
Softcover reprint of hardcover 1st ed. 1997
Pages:
418
Product dimensions:
6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

Foreword to the English Translation. Preface. From the Preface to 'Introduction to the Theory of Cubature Formulas'. 1. Problems and Results of the Theory of Cubature Formulas. 2. Cubature Formulas of Finite Order. 3. Formulas with Regular Boundary Layer for Rational Polyhedra. 4. The Rate of Convergence of Cubature Formulas. 5. Cubature Formulas with Regular Boundary Layer. 6. Universal Asymptotic Optimality. 7. Cubature Formulas of Infinite Order. 8. Functions of A Discrete Variable. 9. Optimal Formulas. References. Notation Index. Subject Index.

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