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Approximate Solution of Operator Equations

  • Authors
  • M. A. Krasnosel’skii
  • G. M. Vainikko
  • P. P. Zabreiko
  • Ya. B. Rutitskii
  • V. Ya. Stetsenko

Table of contents

  1. Front Matter
    Pages i-xii
  2. M. A. Krasnosel’skii, G. M. Vainikko, P. P. Zabreiko, Ya. B. Rutitskii, V. Ya. Stetsenko
    Pages 1-69
  3. M. A. Krasnosel’skii, G. M. Vainikko, P. P. Zabreiko, Ya. B. Rutitskii, V. Ya. Stetsenko
    Pages 70-137
  4. M. A. Krasnosel’skii, G. M. Vainikko, P. P. Zabreiko, Ya. B. Rutitskii, V. Ya. Stetsenko
    Pages 138-198
  5. M. A. Krasnosel’skii, G. M. Vainikko, P. P. Zabreiko, Ya. B. Rutitskii, V. Ya. Stetsenko
    Pages 199-321
  6. M. A. Krasnosel’skii, G. M. Vainikko, P. P. Zabreiko, Ya. B. Rutitskii, V. Ya. Stetsenko
    Pages 322-463
  7. Back Matter
    Pages 464-484

About this book

Introduction

One of the most important chapters in modern functional analysis is the theory of approximate methods for solution of various mathematical problems. Besides providing considerably simplified approaches to numerical methods, the ideas of functional analysis have also given rise to essentially new computation schemes in problems of linear algebra, differential and integral equations, nonlinear analysis, and so on. The general theory of approximate methods includes many known fundamental results. We refer to the classical work of Kantorovich; the investigations of projection methods by Bogolyubov, Krylov, Keldysh and Petrov, much furthered by Mikhlin and Pol'skii; Tikho­ nov's methods for approximate solution of ill-posed problems; the general theory of difference schemes; and so on. During the past decade, the Voronezh seminar on functional analysis has systematically discussed various questions related to numerical methods; several advanced courses have been held at Voronezh Uni­ versity on the application of functional analysis to numerical mathe­ matics. Some of this research is summarized in the present monograph. The authors' aim has not been to give an exhaustive account, even of the principal known results. The book consists of five chapters.

Keywords

Hilbert space approximation distribution functional analysis perturbation perturbation theory

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-010-2715-1
  • Copyright Information Springer Science+Business Media B.V. 1972
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-94-010-2717-5
  • Online ISBN 978-94-010-2715-1
  • Buy this book on publisher's site
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