Theory of Linear Ill-Posed Problems and its Applications / / Valentin K. Ivanov, Vladimir V. Vasin, Vitalii P. Tanana.

• Superior document: Title is part of eBook package: De Gruyter DGBA Backlist Complete English Language 2000-2014 PART1
• VerfasserIn: Ivanov, Valentin K.,; Tanana, Vitalii P.,; Vasin, Vladimir V.,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2013]; ©2002
• Year of Publication: 2013
• Edition: Reprint 2013
• Language: English
• Series: Inverse and Ill-Posed Problems Series , 36
• Physical Description: 1 online resource (281 p.)

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.

Table of Contents

Frontmatter -- Preface to the Second Edition -- Preface -- Contents -- Introduction -- Chapter 1. Well-posedness of problems -- Chapter 2. Regularizing family of operators and sets of uniform regularization -- Chapter 3. Basic techniques for constructing regularizing algorithms -- Chapter 4. Optimality and stability of methods for solving ill-posed problems. Error estimation -- Chapter 5. Determination of values of unbounded operators -- Chapter 6. Finite-dimensional approximation of regulirizing algorithms -- Bibliography -- Additional Bibliography to the Second Edition -- Comments to Additional Bibliography -- Index