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Stable gradient–type iterative methods for smooth irregular operator equations and their application to the problem of acoustic sounding

Mihail Yu. Kokurin, Alexander I. Kozlov


In this paper we present a general scheme for constructing stable iterative methods to solve nonlinear irregular equations with smooth operators in a Hilbert space. The approach is based on restricting Tikhonov’s functional with a nonnegative regularization parameter to an appropriate finite–dimensional affine subspace. In the subspace we search for a domain where the functional is strongly convex and has an unconstrained local minimizer. The minimizer serves as an approximation to a solution of the original equation. The application of relaxational iterative processes to local finite–dimensional minimization of Tikhonov’s functional generates a class of stable iterative methods for nonlinear irregular equations with arbitrary smooth operators. The suggested scheme is demonstrated by solving a model 3D problem of acoustic sounding.


irregular equations, iterative methods, stable iterations, inverse problems, acoustic scattering.

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