Mathematics and Its Applications

Numerical Methods for the Solution of Ill-Posed Problems

Authors: Tikhonov, A.N., Goncharsky, A., Stepanov, V.V., Yagola, A.G.

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About this book

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.

Table of contents (5 chapters)

Table of contents (5 chapters)
  • Introduction

    Pages 1-5

    Tikhonov, A. N. (et al.)

  • Regularization methods

    Pages 7-63

    Tikhonov, A. N. (et al.)

  • Numerical methods for the approximate solution of ill-posed problems on compact sets

    Pages 65-79

    Tikhonov, A. N. (et al.)

  • Algorithms for the approximate solution of ill-posed problems on special sets

    Pages 81-96

    Tikhonov, A. N. (et al.)

  • Algorithms and programs for solving linear ill-posed problems

    Pages 97-161

    Tikhonov, A. N. (et al.)

Buy this book

eBook n/a
  • ISBN 978-94-015-8480-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
Hardcover n/a
  • ISBN 978-0-7923-3583-2
  • Free shipping for individuals worldwide
Softcover n/a
  • ISBN 978-90-481-4583-6
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
Numerical Methods for the Solution of Ill-Posed Problems
Authors
Series Title
Mathematics and Its Applications
Series Volume
328
Copyright
1995
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-94-015-8480-7
DOI
10.1007/978-94-015-8480-7
Hardcover ISBN
978-0-7923-3583-2
Softcover ISBN
978-90-481-4583-6
Edition Number
1
Number of Pages
IX, 253
Additional Information
Originally published in Russian
Topics