Numerical Methods for the Solution of Ill-Posed Problems

  • A. N. Tikhonov
  • A. V. Goncharsky
  • V. V. Stepanov
  • A. G. Yagola

Part of the Mathematics and Its Applications book series (MAIA, volume 328)

Table of contents

  1. Front Matter
    Pages i-ix
  2. A. N. Tikhonov, A. V. Goncharsky, V. V. Stepanov, A. G. Yagola
    Pages 1-5
  3. A. N. Tikhonov, A. V. Goncharsky, V. V. Stepanov, A. G. Yagola
    Pages 7-63
  4. A. N. Tikhonov, A. V. Goncharsky, V. V. Stepanov, A. G. Yagola
    Pages 65-79
  5. A. N. Tikhonov, A. V. Goncharsky, V. V. Stepanov, A. G. Yagola
    Pages 81-96
  6. A. N. Tikhonov, A. V. Goncharsky, V. V. Stepanov, A. G. Yagola
    Pages 97-161
  7. Back Matter
    Pages 163-253

About this book

Introduction

Many problems in science, technology and engineering are posed in the form of operator equations of the first kind, with the operator and RHS approximately known. But such problems often turn out to be ill-posed, having no solution, or a non-unique solution, and/or an unstable solution. Non-existence and non-uniqueness can usually be overcome by settling for `generalised' solutions, leading to the need to develop regularising algorithms.
The theory of ill-posed problems has advanced greatly since A. N. Tikhonov laid its foundations, the Russian original of this book (1990) rapidly becoming a classical monograph on the topic. The present edition has been completely updated to consider linear ill-posed problems with or without a priori constraints (non-negativity, monotonicity, convexity, etc.).
Besides the theoretical material, the book also contains a FORTRAN program library.
Audience: Postgraduate students of physics, mathematics, chemistry, economics, engineering. Engineers and scientists interested in data processing and the theory of ill-posed problems.

Keywords

Fortran algorithms mathematics numerical method

Authors and affiliations

  • A. N. Tikhonov
    • 1
  • A. V. Goncharsky
    • 1
  • V. V. Stepanov
    • 1
  • A. G. Yagola
    • 1
  1. 1.Moscow State UniversityMoscowRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-015-8480-7
  • Copyright Information Springer Science+Business Media B.V. 1995
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-4583-6
  • Online ISBN 978-94-015-8480-7
  • About this book