Overview
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.
Full Product Details
Author: A.B. Bakushinsky ,
M.Yu. Kokurin
Publisher: Springer
Imprint: Springer
Edition: Softcover reprint of hardcover 1st ed. 2004
Volume: 577
Dimensions:
Width: 16.00cm
, Height: 1.60cm
, Length: 24.00cm
Weight: 0.474kg
ISBN: 9789048167982
ISBN 10: 9048167981
Pages: 291
Publication Date: 08 December 2010
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Paperback
Publisher's Status: Active
Availability: Out of stock
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Reviews
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)
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)
"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)"
