Iterative Methods for Approximate Solution of Inverse Problems

A. B. Bakushinsky, M. Yu. Kokurin (auth.)9781402031212, 1-4020-3121-1, 1-4020-3122-X

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.

Table of contents :
Front Matter….Pages i-xv
Irregular Equations As Ill–Posed Problems….Pages 1-15
Regularization Methods For Linear Equations….Pages 17-87
Parametric Approximations Of Solutions To Nonlinear Operator Equations….Pages 89-105
Iterative Processes On The Basis Of Parametric Approximations….Pages 107-157
Stable Iterative Processes….Pages 159-223
Applications Of Iterative Methods….Pages 225-273
Back Matter….Pages 275-291