Geodesic
Levenberg--Marquardt method and its modified versions for solving nonlinear equations with application to the inverse gravimetry problem
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 2, pp. 53-61

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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.
Mots-clés : Levenberg–Marquardt method, a priori information
Keywords: modified process, inverse gravimetry problem. 
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     author = {V. V. Vasin and G. Ya. Perestoronina},
     title = {Levenberg--Marquardt method and its modified versions for solving nonlinear equations with application to the inverse gravimetry problem},
     journal = {Trudy Instituta matematiki i mehaniki},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2011_17_2_a4/}
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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 Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 2, pp. 53-61. http://geodesic.mathdoc.fr/item/TIMM_2011_17_2_a4/