Banach空间中非线性不适定问题的Levenberg-Marquardt迭代法  

Levenberg-Marquardt Iteration Method of Nonlinear Ill-posed Problems in Banach Spaces

作　　者：杨茜[1] 季光明[1] 郭二玲[1] 

机构地区：[1]成都理工大学管理科学学院,成都610059

出　　处：《鲁东大学学报（自然科学版）》2013年第2期106-110,133,共6页Journal of Ludong University:Natural Science Edition

摘　　要：基于已有的Banach空间非线性不适定问题的迭代法,给出了Levenberg-Marquardt迭代法的表达式,研究了它的收敛性.利用先验条件、源条件和广义的Bregman距离,分别证明了Levenberg-Marquardt迭代法的强收敛性和关于Bregman距离的收敛性.Based on the iteration method of nonlinear ill-posed problems in Banach spaces, the expression of Levenberg-Marquardt iteration method is given and the convergence for this kind of method is investigated. The strong convergence of Levenberg-Marquardt iteration method and the convergence with respect to the Bregman distance are proved under a priori parameter, a source condition and the generalized Bregman distance.

关 键 词：不适定问题 Levenberg Marquardt迭代法 Bregman距离 收敛率 

分 类 号：O178[理学—数学]