Iterative Methods for Approximate Solution of Inverse Problems: 577 (Mathematics and Its Applications) - Softcover

Bakushinsky, A.B. B.; Kokurin, M.Yu.

Softcover

ISBN 10: 9048167981 ISBN 13: 9789048167982

Verlag: Springer, 2010

Inhaltsangabe

This volume presents a novel approach to constructing and studying iterative methods for approximate solution of nonlinear inverse problems. It gives a rigorous theoretical analysis of the methods applied, and contains the authors' recent results as well as a comprehensive comparison of related results obtained by leading mathematicians. The approach taken does not require any structural conditions on equations under consideration, except for standard smoothness conditions, and the book can be read by anyone with a basic knowledge of functional analysis.

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Críticas

From the reviews of the first edition:

"This book gives an overview on iterative regularization techniques for the solution of nonlinear inverse problems. Bakushinsky has made significant contributions to this area for some time, and many of these important results are collected in this book. The methods are analyzed on a sound mathematical functional analytical basis." (Otmar Scherzer, Mathematical Reviews, Issue 2006 e)

Reseña del editor

This volume presents a unified approach to constructing iterative methods for solving irregular operator equations and provides rigorous theoretical analysis for several classes of these methods. The analysis of methods includes convergence theorems as well as necessary and sufficient conditions for their convergence at a given rate. The principal groups of methods studied in the book are iterative processes based on the technique of universal linear approximations, stable gradient-type processes, and methods of stable continuous approximations. Compared to existing monographs and textbooks on ill-posed problems, the main distinguishing feature of the presented approach is that it doesn't require any structural conditions on equations under consideration, except for standard smoothness conditions. This allows to obtain in a uniform style stable iterative methods applicable to wide classes of nonlinear inverse problems. Practical efficiency of suggested algorithms is illustrated in application to inverse problems of potential theory and acoustic scattering.

The volume can be read by anyone with a basic knowledge of functional analysis.

The book will be of interest to applied mathematicians and specialists in mathematical modeling and inverse problems.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2010
• ISBN 10: 9048167981
• ISBN 13: 9789048167982
• Einband: Tapa blanda
• Sprache: Englisch
• Anzahl der Seiten: 308
• Kontakt zum Hersteller: Nicht verfügbar