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Trudy Inst. Mat. i Mekh. UrO RAN, 2013, Volume 19, Number 2, Pages 85–97 (Mi timm935)  

This article is cited in 5 scientific papers (total in 5 papers)

Modified Newton-type processes generating Fejér approximations of regularized solutions to nonlinear equations

V. V. Vasinab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Institute of Mathematics and Computer Science, Ural Federal University

Abstract: 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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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2014, 284, suppl. 1, 145–158

Bibliographic databases:

UDC: 517.988.68
Received: 11.02.2013

Citation: V. V. Vasin, “Modified Newton-type processes generating Fejér approximations of regularized solutions to nonlinear equations”, Trudy Inst. Mat. i Mekh. UrO RAN, 19, no. 2, 2013, 85–97; Proc. Steklov Inst. Math. (Suppl.), 284, suppl. 1 (2014), 145–158

Citation in format AMSBIB
\by V.~V.~Vasin
\paper Modified Newton-type processes generating Fej\'er approximations of regularized solutions to nonlinear equations
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2013
\vol 19
\issue 2
\pages 85--97
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2014
\vol 284
\issue , suppl. 1
\pages 145--158

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    This publication is cited in the following articles:
    1. V. V. Vasin, E. N. Akimova, A. F. Miniakhmetova, “Iteratsionnye algoritmy nyutonovskogo tipa i ikh prilozheniya k obratnoi zadache gravimetrii”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 6:3 (2013), 26–37  mathnet
    2. Vasin V., George S., “An Analysis of Lavrentiev Regularization Method and Newton Type Process for Nonlinear Ill-Posed Problems”, Appl. Math. Comput., 230 (2014), 406–413  crossref  mathscinet  zmath  isi  elib  scopus
    3. V. S. Shubha, S. George, P. Jidesh, M. E. Shobha, “Finite Dimensional Realization of a Quadratic Convergence Yielding Iterative Regularization Method For Ill-Posed Equations With Monotone Operators”, Appl. Math. Comput., 273 (2016), 1041–1050  crossref  mathscinet  isi  elib  scopus
    4. N. Yaparova, “Method For Temperature Measuring in the Rod With Heat Source Under Uncertain Initial Temperature”, 2016 2nd International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM), IEEE, 2016  isi
    5. V. V. Vasin, “Iterative processes for ill-posed problems with a monotone operator”, Siberian Adv. Math., 29 (2019), 217–229  mathnet  crossref  crossref
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