The Levenberg-Marquardt method and its modified versions for solving nonlinear equations with application to the inverse gravimetry problem / Vasin V. V.,Perestoronina G. Ya // PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS. - 2013. - V. 280, l. 1. - P. 174-182.

ISSN/EISSN:

0081-5438 / 1531-8605

Type:

Article

Abstract:

The Levenberg-Marquardt method and its modified versions are studied. Under some local conditions on the operator (in a neighborhood of a solution), strong and weak convergence of iterations is established with the solution error monotonically decreasing. The conditions are shown to be true for one class of nonlinear integral equations, in particular, for the structural gravimetry problem. Results of model numerical experiments for the inverse nonlinear gravimetry problem are presented.

Author keywords:

Levenberg-Marquardt method; modified process; a priori information; inverse gravimetry problem

DOI:

10.1134/S0081543813020144

Web of Science ID:

ISI:000317236500014

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
Research-Areas	Mathematics
Web-of-Science-Categories	Mathematics, Applied; Mathematics
Author-Email	vasin@imm.uran.ru pgja@imm.uran.ru
Funding-Acknowledgement	Russian Foundation for Basic Research {[}09-01-00053]; Ural Branch of the Russian Academy of Sciences within Interdisciplinary project {[}09-M-15-2001]
Funding-Text	This work was supported by the Russian Foundation for Basic Research (project no. 09-01-00053) and by the Ural Branch of the Russian Academy of Sciences within Interdisciplinary project no. 09-M-15-2001.
Number-of-Cited-References	8
Usage-Count-Since-2013	5
Journal-ISO	Proc. Steklov Inst. Math.
Doc-Delivery-Number	121IL