Overview
- Presents a novel approach to constructing and studying iterative methods for approximate solution of nonlinear inverse problems
- Gives rigorous theoretical analysis of the methods
- Contains authors' recent results as well as a comprehensive comparison of related results obtained by leading mathematicians
Part of the book series: Mathematics and Its Applications (MAIA, volume 577)
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Table of contents (6 chapters)
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Front Matter
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Back Matter
Keywords
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)
Authors and Affiliations
Bibliographic Information
Book Title: Iterative Methods for Approximate Solution of Inverse Problems
Authors: A. B. Bakushinsky, M. Yu. Kokurin
Series Title: Mathematics and Its Applications
DOI: https://doi.org/10.1007/978-1-4020-3122-9
Publisher: Springer Dordrecht
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eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media B.V. 2004
Hardcover ISBN: 978-1-4020-3121-2Published: 15 February 2005
Softcover ISBN: 978-90-481-6798-2Published: 08 December 2010
eBook ISBN: 978-1-4020-3122-9Published: 28 September 2007
Edition Number: 1
Number of Pages: XV, 291
Topics: Numerical Analysis, Algorithms, Integral Equations, Partial Differential Equations, Mathematical Modeling and Industrial Mathematics