Theory of Linear Ill-Posed Problems and its Applications
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Valentin K. Ivanov
About this book
This monograph is a revised and extended version of the Russian edition from 1978. It includes the general theory of linear ill-posed problems concerning e. g. the structure of sets of uniform regularization, the theory of error estimation, and the optimality method. As a distinguishing feature the book considers ill-posed problems not only in Hilbert but also in Banach spaces.
It is natural that since the appearance of the first edition considerable progress has been made in the theory of inverse and ill-posed problems as wall as in ist applications. To reflect these accomplishments the authors included additional material e. g. comments to each chapter and a list of monographs with annotations.
Author / Editor information
Valentin K. Ivanov †; Vladimir V. Vasin, Institute of Mathematics and Mechanics, Russian Academy of Sciences, Ekaterinburg, Russia; Vitalii P. Tanana, South Ural State University, Chelyabinsk, Russia.
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Frontmatter
i -
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Preface to the Second Edition
vii -
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Preface
ix -
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Contents
xi -
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Introduction
1 -
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Chapter 1. Well-posedness of problems
5 -
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Chapter 2. Regularizing family of operators and sets of uniform regularization
47 -
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Chapter 3. Basic techniques for constructing regularizing algorithms
71 -
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Chapter 4. Optimality and stability of methods for solving ill-posed problems. Error estimation
135 -
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Chapter 5. Determination of values of unbounded operators
185 -
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Chapter 6. Finite-dimensional approximation of regulirizing algorithms
213 -
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Bibliography
243 -
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Additional Bibliography to the Second Edition
259 -
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Comments to Additional Bibliography
265 -
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Index
279
