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Trudy Inst. Mat. i Mekh. UrO RAN, 2011, Volume 17, Number 2, Pages 53–61 (Mi timm695)  

This article is cited in 7 scientific papers (total in 8 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

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.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2013, 280, suppl. 1, 174–182

Bibliographic databases:

UDC: 517.988.68
Received: 19.10.2010

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. (Suppl.), 280, suppl. 1 (2013), 174–182

Citation in format AMSBIB
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\paper Levenberg--Marquardt method and its modified versions for solving nonlinear equations with application to the inverse gravimetry problem
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2011
\vol 17
\issue 2
\pages 53--61
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\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2013
\vol 280
\issue , suppl. 1
\pages 174--182
\crossref{https://doi.org/10.1134/S0081543813020144}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. V. Vasin, “The Levenberg–Marquardt method for approximation of solutions of irregular operator equations”, Autom. Remote Control, 73:3 (2012), 440–449  mathnet  crossref  isi
    2. “Vladimir Vasil'evich Vasin. On the occasion of his 70th birsday”, Proc. Steklov Inst. Math. (Suppl.), 280, suppl. 1 (2013), 1–12  mathnet  crossref  isi
    3. Vasin V., “Irregular Nonlinear Operator Equations: Tikhonov's Regularization and Iterative Approximation”, J. Inverse Ill-Posed Probl., 21:1 (2013), 109–123  crossref  mathscinet  zmath  isi  elib  scopus
    4. 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
    5. Chaari A., Giraud-Moreau L., Grosges T., Barchiesi D., “Numerical Modeling of the Photothermal Processing for Bubble Forming Around Nanowire in a Liquid”, Sci. World J., 2014, 794630  crossref  isi  scopus
    6. Babanov Yu., Salamatov Yu., Ustinov V., “a New Interpretation of X-Ray Reflectivity in Real Space For Low Contrast Multilayer Systems i. Mathematical Algorithm and Numerical Simulations”, Superlattices Microstruct., 74 (2014), 100–113  crossref  isi  elib  scopus
    7. Babanov Yu.A., Salamatov Yu.A., Ustinov V.V., Mukhamedzhanov E.Kh., “Diagnostics of the Atomic Structure of Multilayer Metallic Nanoheterostructures From Reflectometry Data: a New Approach To Low-Contrast Systems”, Phys. Solid State, 56:9 (2014), 1904–1915  crossref  isi  elib  scopus
    8. A. F. Skurydina, “A regularized Levenberg–Marquardt type method applied to the structural inverse gravity problem in a multilayer medium and its parallel realization”, Vestn. YuUrGU. Ser. Vych. matem. inform., 6:3 (2017), 5–15  mathnet  crossref  elib
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