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

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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 (Supplementary issues), 2013, Volume 280, Issue 1, Pages 174–182
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. (Suppl.), 280, suppl. 1 (2013), 174–182

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/timm695

https://www.mathnet.ru/eng/timm/v17/i2/p53

This publication is cited in the following 14 articles:

Rafał Brociek, Edyta Hetmaniok, Christian Napoli, Giacomo Capizzi, Damian Słota, “Identification of aerothermal heating for thermal protection systems taking into account the thermal resistance between layers”, International Journal of Heat and Mass Transfer, 218 (2024), 124772
V. Lukianenko, M. Kozlova, V. Belozub, “Application of Wavelet Transform to Urysohn-Type Equations”, Mathematics, 11:18 (2023), 3999
Rafał Brociek, Edyta Hetmaniok, Christian Napoli, Giacomo Capizzi, Damian Słota, “Estimation of aerothermal heating for a thermal protection system with temperature dependent material properties”, International Journal of Thermal Sciences, 188 (2023), 108229
Junpeng Zhou, Letang Xue, Yan Li, Lihua Cao, Changqing Chen, “A Novel Fuzzy Controller for Visible-Light Camera Using RBF-ANN: Enhanced Positioning and Autofocusing”, Sensors, 22:22 (2022), 8657
V Belozub, M Kozlova, V Lukianenko, “Approximated solution algorithms for Urysohn-type equations”, J. Phys.: Conf. Ser., 1902:1 (2021), 012051
Xiang Gao, Gang Xu, Muye Pang, Biwei Tang, Kui Xiang, 2021 6th IEEE International Conference on Advanced Robotics and Mechatronics (ICARM), 2021, 639
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
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
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
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
Vasin V., “Irregular Nonlinear Operator Equations: Tikhonov's Regularization and Iterative Approximation”, J. Inverse Ill-Posed Probl., 21:1 (2013), 109–123
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
V. V. Vasin, “The Levenberg–Marquardt method for approximation of solutions of irregular operator equations”, Autom. Remote Control, 73:3 (2012), 440–449
“Vladimir Vasil'evich Vasin. On the occasion of his 70th birsday”, Proc. Steklov Inst. Math. (Suppl.), 280, suppl. 1 (2013), 1–12

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