ENGLISH

Iterative Methods for Approximate Solution of Inverse Problems

By A. B. Bakushinsky , M. Yu. Kokurin (auth.)

Book information

Publisher
Springer Netherlands
Year
2004
ISBN
1402031211, 9781402031212, 140203122X
DOI
10.1007/978-1-4020-3122-9
LCC
QA297.8 .B34 2004
Open Library ID
OL3435860M
Language
english
Format
PDF
Filesize
1 MB (1303636 bytes)
Series
Mathematics and Its Applications 577
Edition
1
Pages
291\298
Library
Kolxo3
Time added
2009-07-20 03:45:11
Numerical Analysis; Algorithms; Integral Equations

Description

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.

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