Modified Newton-Type Processes Generating Fejer Approximations of Regularized Solutions to Nonlinear Equations / Vasin V. V. // PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS. - 2014. - V. 284, l. 1. - P. S145-S158.

ISSN/EISSN:

0081-5438 / 1531-8605

Type:

Article

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 the 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.

Author keywords:

irregular operator equations; modified Newton-type method; Fejer approximation. ILL-POSED PROBLEMS; CONVERGENCE

DOI:

10.1134/S0081543814020138

Web of Science ID:

ISI:000334277400013

Соавторы в МНС:

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Другие поля

Поле	Значение
Month	APR
Publisher	MAIK NAUKA/INTERPERIODICA/SPRINGER
Address	233 SPRING ST, NEW YORK, NY 10013-1578 USA
Language	English
EISSN	1531-8605
Keywords-Plus	ILL-POSED PROBLEMS; CONVERGENCE
Research-Areas	Mathematics
Web-of-Science-Categories	Mathematics, Applied; Mathematics
Author-Email	vasin@imm.uran.ru
Funding-Acknowledgement	Government of the Russian Federation {[}11.G34.31.0064]; Russian Foundation for Basic Research {[}12-01-00106]; Ural Branch of the Russian Academy of Sciences {[}12-P-15-2019]; Program for State Support of Leading Universities of the Russian Federation {[}02.A03.21.0006]
Funding-Text	This work was supported by a grant of the Government of the Russian Federation (contract no. 11.G34.31.0064), by the Russian Foundation for Basic Research (project no. 12-01-00106), by the Ural Branch of the Russian Academy of Sciences (project no. 12-P-15-2019), and by the Program for State Support of Leading Universities of the Russian Federation (agreement no. 02.A03.21.0006 of August 27, 2013).
Number-of-Cited-References	20
Journal-ISO	Proc. Steklov Inst. Math.
Doc-Delivery-Number	AE8UG