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.
General
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