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Regularization of Inverse Problems

  • Fester Einband
  • 332 Seiten
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Driven by the needs of applications both in sciences and in industry, the field of inverse problems has certainly been one of the ... Weiterlesen
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Beschreibung

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.

Zusammenfassung
This book is devoted to the mathematical theory of regularization methods and gives an account of the currently available results about regularization methods for linear and nonlinear ill-posed problems.

Inhalt

Preface. 1. 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.

Produktinformationen

Titel: Regularization of Inverse Problems
Autor:
EAN: 9780792341574
ISBN: 0792341570
Format: Fester Einband
Herausgeber: Springer Netherlands
Genre: Mathematik
Anzahl Seiten: 332
Gewicht: 666g
Größe: H240mm x B161mm x T23mm
Jahr: 1996
Auflage: 1996

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