Published by De Gruyter 2002

Theory of Linear Ill-Posed Problems and its Applications

Valentin K. Ivanov , Vladimir V. Vasin and Vitalii P. Tanana

Volume 36 in the series Inverse and Ill-Posed Problems Series

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.

Topics

Frontmatter Publicly Available Download PDF	i
Preface to the Second Edition Requires Authentication Unlicensed Licensed Download PDF	vii
Preface Requires Authentication Unlicensed Licensed Download PDF	ix
Contents Publicly Available Download PDF	xi
Introduction Requires Authentication Unlicensed Licensed Download PDF	1
Chapter 1. Well-posedness of problems Requires Authentication Unlicensed Licensed Download PDF	5
Chapter 2. Regularizing family of operators and sets of uniform regularization Requires Authentication Unlicensed Licensed Download PDF	47
Chapter 3. Basic techniques for constructing regularizing algorithms Requires Authentication Unlicensed Licensed Download PDF	71
Chapter 4. Optimality and stability of methods for solving ill-posed problems. Error estimation Requires Authentication Unlicensed Licensed Download PDF	135
Chapter 5. Determination of values of unbounded operators Requires Authentication Unlicensed Licensed Download PDF	185
Chapter 6. Finite-dimensional approximation of regulirizing algorithms Requires Authentication Unlicensed Licensed Download PDF	213
Bibliography Requires Authentication Unlicensed Licensed Download PDF	243
Additional Bibliography to the Second Edition Requires Authentication Unlicensed Licensed Download PDF	259
Comments to Additional Bibliography Requires Authentication Unlicensed Licensed Download PDF	265
Index Requires Authentication Unlicensed Licensed Download PDF	279

(Deutsch)

Language: English
Publisher: De Gruyter
Edition: Reprint 2013
Audience: Students, R3esearchers, and Lecturers in Mathematics; Academic Libraries
Pages
- Front matter: 13
- Main content: 281
Illustrations
- Illustrations: 5
Keywords: Linear Ill-posed Problems; Sets of Uniform Regularization; Error Estimation; Optimality Method; Hilbert Spaces; Banach spaces

eBook

Published: February 18, 2013
ISBN: 9783110944822