Regularization of Inverse Problems

Engl, Heinz W. (Institut f. Mathematik, Johannes Kepler Universitat, Linz, Austria); Hanke, Martin; Neubauer, A. (Johannes Kepler Universitat, Linz,

ISBN 10: 0792361407 / ISBN 13: 9780792361404

Published by Kluwer Academic Publishers, 2000

About this Item

Describes mathematical theory of regularization methods. This book presents regularization methods for linear and nonlinear ill-posed problems. It considers both continuous and iterative regularization methods with special emphasis on the development of parameter choice and stopping rules which lead to optimal convergence rates. Series: Mathematics and its Applications. Num Pages: 322 pages, biography. BIC Classification: PBKS. Category: (G) General (US: Trade); (P) Professional & Vocational. Dimension: 234 x 156 x 17. Weight in Grams: 467. . 2000. Softcover reprint of the original 1st ed. 2000. Paperback. . . . .

Seller Inventory # V9780792361404

Bibliographic Details

• Title: Regularization of Inverse Problems
• Publisher: Kluwer Academic Publishers
• Publication Date: 2000
• Language: English
• ISBN 10: 0792361407
• ISBN 13: 9780792361404
• Binding: Soft cover
• Condition: New

About this title

Synopsis

In the last two decades, the field of inverse problems has certainly been one of the fastest growing areas in applied mathematics. This growth has largely been driven by the needs of applications both in other sciences and in industry. In Chapter 1, we will give a short overview over some classes of inverse problems of practical interest. Like everything in this book, this overview is far from being complete and quite subjective. As will be shown, inverse problems typically lead to mathematical models that are not well-posed in the sense of Hadamard, i.e., to ill-posed problems. This means especially that their solution is unstable under data perturbations. Numerical meth­ ods that can cope with this problem are the so-called regularization methods. This book is devoted to the mathematical theory of regularization methods. For linear problems, this theory can be considered to be relatively complete and will be de­ scribed in Chapters 2 - 8. For nonlinear problems, the theory is so far developed to a much lesser extent. We give an account of some of the currently available results, as far as they might be of lasting value, in Chapters 10 and 11. Although the main emphasis of the book is on a functional analytic treatment in the context of operator equations, we include, for linear problems, also some information on numerical aspects in Chapter 9.

Review

`It is written in a very clear style, the material is well organized, and there is an extensive bibliography with 290 items. There is no doubt that this book belongs to the modern standard references on ill-posed and inverse problems. It can be recommended not only to mathematicians interested in this, but to students with a basic knowledge of functional analysis, and to scientists and engineers working in this field.'
Mathematical Reviews Clippings, 97k
`... it will be an extremely valuable tool for researchers in the field, who will find under the same cover and with unified notation material that is otherwise scattered in extremely diverse publications.'
SIAM Review, 41:2 (1999)