Regularization of Ill-Posed Problems by Iteration Methods by S.F. GilyazovRegularization of Ill-Posed Problems by Iteration Methods by S.F. Gilyazov

Regularization of Ill-Posed Problems by Iteration Methods

byS.F. Gilyazov, N.l. Gol'dman

Paperback | December 9, 2010

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This volume presents new results in regularization of ill-posed problems by iteration methods, which is one of the most important and rapidly developing topics of the theory of ill-posed problems. The new theoretical results are connected with the proposed united approach to the proof of regularizing properties of the `classical' iteration methods (steepest descent, conjugate direction) complemented by the stopping rule depending on the level of errors in the input data. Much emphasis is given to the choice of the iteration index as the regularization parameter and to the rate convergence estimates of the approximate solutions. Results of calculations for important applications in non-linear thermophysics are also presented. Audience: This work will be a useful resource for specialists in the theory of partial differential and integral equations, in numerical analysis and in theory and methods.
Title:Regularization of Ill-Posed Problems by Iteration MethodsFormat:PaperbackDimensions:351 pagesPublished:December 9, 2010Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048153824

ISBN - 13:9789048153824

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Table of Contents

Preface. Introduction. 1. Regularizing Algorithms for Linear Ill-Posed Problems: Unified Approach. 2. Iteration Steepest Descent Methods for Linear Operator Equations. 3. Iteration Conjugate Direction Methods For Linear Operator Equations. 4. Iteration Steepest Descent Methods for Nonlinear Operator Equations. 5. Iteration Methods for Ill-Posed Constrained Minimization Problems. 6. Descriptive Regularization Algorithms on the Basis of the Conjugate Gradient Projection Method. Bibliography. Index.

Editorial Reviews

`The book will be useful for specialists who in their theoretical and applied investigations deal with ill-posed and inverse problems.' Mathematical Reviews Clippings (2001)