Bibliographic Information

The theory of cubature formulas

by S.L. Sobolev and V.L. Vaskevich

(Mathematics and its applications, v. 415)

Kluwer, Academic Publishers, 1997

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Note

Bibliography: p. [389]-410

Includes index

Description and Table of Contents

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.

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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Details

  • NCID
    BA31679618
  • ISBN
    • 0792346319
  • LCCN
    97017691
  • Country Code
    ne
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Original Language Code
    rus
  • Place of Publication
    Dordrecht ; Boston
  • Pages/Volumes
    xxi, 416 p.
  • Size
    25 cm
  • Classification
  • Subject Headings
  • Parent Bibliography ID
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