This article is cited in 6 papers

Iteratively regularized methods for irregular nonlinear operator equations with a normally solvable derivative at the solution

M. Yu. Kokurin

Mari State University, Yoshkar-Ola, Russia

Abstract: A group of iteratively regularized methods of Gauss–Newton type for solving irregular nonlinear equations with smooth operators in a Hilbert space under the condition of normal solvability of the derivative of the operator at the solution is considered. A priori and a posteriori methods for termination of iterations are studied, and estimates of the accuracy of approximations obtained are found. It is shown that, in the case of a priori termination, the accuracy of the approximation is proportional to the error in the input data. Under certain additional conditions, the same estimate is established for a posterior termination from the residual principle. These results generalize known similar estimates for linear equations with a normally solvable operator.

Key words: operator equations, irregular operator, Hilbert space, normally solvable operator, Gauss–Newton methods, iterative regularization, termination criterion, estimate of accuracy.

UDC: 519.642.8

Received: 28.10.2015
Revised: 16.02.2016

DOI: 10.7868/S0044466916090106

 English version: Computational Mathematics and Mathematical Physics, 2016, 56:9, 1523–1535

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