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

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.