Geodesic
Modified Newton-type processes generating Fej\'er approximations of regularized solutions to nonlinear equations
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 2, pp. 85-97

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We investigate a two-stage algorithm for the construction of a regularizing algorithm that solves approximately a nonlinear irregular operator equation. First, the initial equation is regularized by a shift (Lavrent'ev's scheme). To approximate a solution of the regularized equation, we apply modified Newton and Gauss–Newton type methods, in which the derivative of the operator is calculated at a fixed point for all iterations. Convergence theorems for the processes, error estimates, and the Fejer property of iterations are established.
Keywords: irregular operator equations, modified Newton-type method, Fejér approximation. 
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     author = {V. V. Vasin},
     title = {Modified {Newton-type} processes generating {Fej\'er} approximations of regularized solutions to nonlinear equations},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {85--97},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2013_19_2_a8/}
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V. V. Vasin. Modified Newton-type processes generating Fej\'er approximations of regularized solutions to nonlinear equations. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 2, pp. 85-97. http://geodesic.mathdoc.fr/item/TIMM_2013_19_2_a8/