Regularization of inverse problems

著者

書誌事項

Regularization of inverse problems

by Heinz W. Engl, Martin Hanke, and Andreas Neubauer

(Mathematics and its applications, v. 375)

Kluwer Academic Publishers, c2000

  • :hb
  • : pbk

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注記

Includes bibliographical references (p. 299-318) and index

内容説明・目次

内容説明

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. 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.

目次

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.

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