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

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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2013, Volume 19, Number 2, Pages 85–97 (Mi timm935)

This article is cited in 8 scientific papers (total in 8 papers)

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

V. V. Vasin^ab

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

Full-text PDF (208 kB) Citations (8)

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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.

Received: 11.02.2013

English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2014, Volume 284, Issue 1, Pages 145–158
DOI: https://doi.org/10.1134/S0081543814020138

Bibliographic databases:

Document Type: Article

UDC: 517.988.68

Language: Russian

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

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https://www.mathnet.ru/eng/timm935

https://www.mathnet.ru/eng/timm/v19/i2/p85

This publication is cited in the following 8 articles:

V. V. Vasin, “Iterative processes for ill-posed problems with a monotone operator”, Siberian Adv. Math., 29 (2019), 217–229
V. V. Vasin, A. F. Skurydina, “A two-stage method of construction of regularizing algorithms for nonlinear ill-posed problems”, Proc. Steklov Inst. Math. (Suppl.), 301:1 (2018), 173–190
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
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
N. Yaparova, 2016 2nd International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM), 2016, 1
V. V. Vasin, “Modified steepest descent method for nonlinear irregular operator equations”, Dokl. Math., 91:3 (2015), 300
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
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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Trudy Instituta Matematiki i Mekhaniki UrO RAN

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References:	66
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