Iterative processes for ill-posed problems with a monotone operator

V. V. Vasin

Matematičeskie trudy, Tome 21 (2018) no. 2, pp. 117-135.

Résumé

We consider the problem on constructing a stable approximate solution of an inverse problem formulated as a nonlinear irregular equation with a monotone operator. We suggest a two-stage method based on Lavrentiev's regularization scheme and iterative approximation with the use of either modified Newton's method or a regularized $\kappa$-process. We prove that the iterative processes converge and the iterations possess the Fejér property. We show that our method generates a regularization algorithm under a certain adjustment of control parameters. On the set of source-like representable solutions, we find an optimal-order error estimate for the algorithm.

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