Geodesic
Iterative processes for ill-posed problems with a monotone operator
Matematičeskie trudy, Tome 21 (2018) no. 2, pp. 117-135

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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. 
@article{MT_2018_21_2_a4,
     author = {V. V. Vasin},
     title = {Iterative processes for ill-posed problems with a monotone operator},
     journal = {Matemati\v{c}eskie trudy},
     pages = {117--135},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2018_21_2_a4/}
}
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V. V. Vasin. Iterative processes for ill-posed problems with a monotone operator. Matematičeskie trudy, Tome 21 (2018) no. 2, pp. 117-135. http://geodesic.mathdoc.fr/item/MT_2018_21_2_a4/