The Theory of Cubature Formulas

  • S. L. Sobolev
  • V. L. Vaskevich

Part of the Mathematics and Its Applications book series (MAIA, volume 415)

Table of contents

  1. Front Matter
    Pages i-ix
  2. S. L. Sobolev, V. L. Vaskevich
    Pages 1-42
  3. S. L. Sobolev, V. L. Vaskevich
    Pages 43-73
  4. S. L. Sobolev, V. L. Vaskevich
    Pages 74-92
  5. S. L. Sobolev, V. L. Vaskevich
    Pages 93-130
  6. S. L. Sobolev, V. L. Vaskevich
    Pages 131-172
  7. S. L. Sobolev, V. L. Vaskevich
    Pages 173-220
  8. S. L. Sobolev, V. L. Vaskevich
    Pages 221-291
  9. S. L. Sobolev, V. L. Vaskevich
    Pages 292-330
  10. S. L. Sobolev, V. L. Vaskevich
    Pages 331-388
  11. Back Matter
    Pages 389-418

About this book

Introduction

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.

Keywords

Numerical integration cubature functional analysis numerical analysis

Authors and affiliations

  • S. L. Sobolev
    • 1
  • V. L. Vaskevich
    • 1
  1. 1.Sobolev Institute of MathematicsSiberian Division of the Russian Academy of SciencesNovosibirskRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-015-8913-0
  • Copyright Information Springer Science+Business Media B.V. 1997
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-4875-2
  • Online ISBN 978-94-015-8913-0
  • About this book
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