Regularization of Inverse Problems
(Sprache: Englisch)
Driven by the needs of applications both in sciences and in industry, the field of inverse problems has certainly been one of the fastest growing areas in applied mathematics recently. This book starts with an overview over some classes of inverse problems...
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Klappentext zu „Regularization of Inverse Problems “
Driven by the needs of applications both in sciences and in industry, the field of inverse problems has certainly been one of the fastest growing areas in applied mathematics recently. This book starts with an overview over some classes of inverse problems of practical interest. Inverse problems typically lead to mathematical models that are ill-posed in the sense of Hadamard. Especially, their solution is unstable under data perturbations, so that special numerical methods that can cope with these instabilities, so-called regularization methods, have to be developed. This book is devoted to the mathematical theory of regularization methods and is intended to give an up-to-date account of the currently available results about regularization methods both for linear and for nonlinear ill-posed problems. Both continuous and iterative regularization methods are considered in detail with special emphasis on the development of parameter choice and stopping rules which lead to optimal convergence rates. Audience: This book, which can be read by students with a basic knowledge of functional analysis, should be useful both to mathematicians and to scientists and engineers who deal with inverse problems in their fields. It can be used as a text for a graduate course on inverse problems and will also be useful to specialists in the field as a reference work.
Inhaltsverzeichnis zu „Regularization of Inverse Problems “
- Preface1. Introduction: Examples of Inverse Problems
2. Ill-Posed Linear Operator Equations
3. Regularization Operators
4. Continuous Regularization Methods
5. Tikhonov Regularization
6. Iterative Regularization Methods
7. The Conjugate Gradient Method
8. Regularization with Differential Operators
9. Numerical Realization
10. Tikhonov Regularization of Nonlinear Problems
11. Iterative Methods for Nonlinear Problems
- A. Appendix: A.1. Weighted Polynomial Minimization Problems
- A.2. Orthogonal Polynomials
- A.3. Christoffel Functions
- Bibliography
- Index
Bibliographische Angaben
- Autoren: Heinz Werner Engl , Martin Hanke , A. Neubauer
- 1996, 322 Seiten, Maße: 16,1 x 24 cm, Gebunden, Englisch
- Verlag: Springer Netherlands
- ISBN-10: 0792341570
- ISBN-13: 9780792341574
- Erscheinungsdatum: 31.07.1996
Sprache:
Englisch
Rezension zu „Regularization of Inverse Problems “
`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)
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