Mathematics and Its Applications

Iterative Methods for Approximate Solution of Inverse Problems

Authors: Bakushinsky, A.B., Kokurin, M.Yu.

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About this book

This volume presents a unified approach to constructing iterative methods for solving irregular operator equations and provides rigorous theoretical analysis for several classes of these methods. The analysis of methods includes convergence theorems as well as necessary and sufficient conditions for their convergence at a given rate. The principal groups of methods studied in the book are iterative processes based on the technique of universal linear approximations, stable gradient-type processes, and methods of stable continuous approximations. Compared to existing monographs and textbooks on ill-posed problems, the main distinguishing feature of the presented approach is that it doesn’t require any structural conditions on equations under consideration, except for standard smoothness conditions. This allows to obtain in a uniform style stable iterative methods applicable to wide classes of nonlinear inverse problems. Practical efficiency of suggested algorithms is illustrated in application to inverse problems of potential theory and acoustic scattering.

The volume can be read by anyone with a basic knowledge of functional analysis.

The book will be of interest to applied mathematicians and specialists in mathematical modeling and inverse problems.

Reviews

From the reviews of the first edition:

"This book gives an overview on iterative regularization techniques for the solution of nonlinear inverse problems. Bakushinsky has made significant contributions to this area for some time, and many of these important results are collected in this book. The methods are analyzed on a sound mathematical functional analytical basis." (Otmar Scherzer, Mathematical Reviews, Issue 2006 e)


Table of contents (6 chapters)

Table of contents (6 chapters)

Buy this book

eBook $84.99
price for USA in USD (gross)
  • ISBN 978-1-4020-3122-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.99
price for USA in USD
  • ISBN 978-1-4020-3121-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.99
price for USA in USD
  • ISBN 978-90-481-6798-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Iterative Methods for Approximate Solution of Inverse Problems
Authors
Series Title
Mathematics and Its Applications
Series Volume
577
Copyright
2004
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media B.V.
eBook ISBN
978-1-4020-3122-9
DOI
10.1007/978-1-4020-3122-9
Hardcover ISBN
978-1-4020-3121-2
Softcover ISBN
978-90-481-6798-2
Edition Number
1
Number of Pages
XV, 291
Topics