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Regularization of Inverse Problems

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  • © 2000
  • Latest edition

Overview

Part of the book series: Mathematics and Its Applications (MAIA, volume 375)

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About this book

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.

Keywords

  • CON_9016
  • partial differential equations

Reviews

`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)

Authors and Affiliations

  • Universität Linz Inst. Industriemathematik, Linz, Austria

    Heinz Werner Engl, A. Neubauer

Bibliographic Information

  • Book Title: Regularization of Inverse Problems

  • Authors: Heinz Werner Engl, Martin Hanke, A. Neubauer

  • Series Title: Mathematics and Its Applications

  • Publisher: Springer Dordrecht

  • eBook Packages: Mathematics and Statistics (R0)

  • Copyright Information: Kluwer Academic Publishers 2000

  • Hardcover ISBN: 978-0-7923-4157-4Published: 31 July 1996

  • Softcover ISBN: 978-0-7923-6140-4Published: 31 March 2000

  • Edition Number: 1

  • Number of Pages: VIII, 322

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