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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2011, Volume 17, Number 2, Pages 53–61 (Mi timm695)  
This article is cited in 13 scientific papers (total in 14 papers)

Levenberg–Marquardt method and its modified versions for solving nonlinear equations with application to the inverse gravimetry problem

V. V. Vasin, G. Ya. Perestoronina

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
Full-text PDF (172 kB) Citations (14)
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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.
Keywords: Levenberg–Marquardt method, modified process, a priori information, inverse gravimetry problem.
Received: 19.10.2010
English version:
Proceedings of the Steklov Institute of Mathematics (Supplement Issues), 2013, Volume 280, Issue 1, Pages S174–S182
DOI: https://doi.org/10.1134/S0081543813020144
Bibliographic databases:
Document Type: Article
UDC: 517.988.68
Language: Russian
Citation: V. V. Vasin, G. Ya. Perestoronina, “Levenberg–Marquardt method and its modified versions for solving nonlinear equations with application to the inverse gravimetry problem”, Trudy Inst. Mat. i Mekh. UrO RAN, 17, no. 2, 2011, 53–61; Proc. Steklov Inst. Math., 280, suppl. 1 (2013), S174–S182
Citation in format AMSBIB
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    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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