naa a22 4500 510811841 CHVBK 20180411083446.0 cr unu---uuuuu 180411e20130401xx s 000 0 eng 10.1134/S0081543813020144 doi (NATIONALLICENCE)springer-10.1134/S0081543813020144 The Levenberg-Marquardt method and its modified versions for solving nonlinear equations with application to the inverse gravimetry problem [Elektronische Daten] [V. Vasin, G. Perestoronina] 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. Pleiades Publishing, Ltd., 2013 Levenberg-Marquardt method nationallicence modified process nationallicence a priori information nationallicence inverse gravimetry problem nationallicence Vasin V. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, 620990, Yekaterinburg, Russia aut Perestoronina G. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, 620990, Yekaterinburg, Russia aut Proceedings of the Steklov Institute of Mathematics SP MAIK Nauka/Interperiodica 280(2013-04-01), 174-182 0081-5438 280<174 2013 280 11501 https://doi.org/10.1134/S0081543813020144 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1134/S0081543813020144 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Vasin V. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, 620990, Yekaterinburg, Russia aut NATIONALLICENCE 700 1- Perestoronina G. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, 620990, Yekaterinburg, Russia aut NATIONALLICENCE 773 0- Proceedings of the Steklov Institute of Mathematics SP MAIK Nauka/Interperiodica 280(2013-04-01), 174-182 0081-5438 280<174 2013 280 11501 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer