The Levenberg-Marquardt method and its modified versions for solving nonlinear equations with application to the inverse gravimetry problem

被引：12
|
作者：
Vasin, V. V. [1 ,2 ]
Perestoronina, G. Ya [1 ]
机构：
[1] Russian Acad Sci, Ural Branch, Inst Math & Mech, Ekaterinburg 620990, Russia
[2] Ural Fed Univ, Inst Math & Comp Sci, Ekaterinburg 620000, Russia
来源：
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS | 2013年 / 280卷
基金：
俄罗斯基础研究基金会;
关键词：
Levenberg-Marquardt method; modified process; a priori information; inverse gravimetry problem;
D O I：
10.1134/S0081543813020144
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
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页码：174 / 182
页数：9
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