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

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

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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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
2. “Vladimir Vasil'evich Vasin. On the occasion of his 70th birsday”, Proc. Steklov Inst. Math. (Suppl.), 280, suppl. 1 (2013), 1–12
3. Vasin V., “Irregular Nonlinear Operator Equations: Tikhonov's Regularization and Iterative Approximation”, J. Inverse Ill-Posed Probl., 21:1 (2013), 109–123
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
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
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
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
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
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