Toward global convergence for strongly nonlinear ill-posed problems via a regularizing multilevel approach

被引:11
作者
Kaltenbacher, Barbara [1 ]
机构
[1] Univ Erlangen Nurnberg, Dept Sensor Technol, Erlangen, Germany
关键词
multilevel method; nonlinear ill-posed problems; regularization;
D O I
10.1080/01630560600790835
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we propose a multilevel method for solving nonlinear ill-posed operator equations By minimizing the distance to some initial guess under the constraint of a discretized version of the operator equation for different levels of discretization, we define a sequence of regularized approximations to the exact solution, which is shown to be stable and convergent for arbitrary initial guess and can be computed via a multilevel procedure that altogether yields a globally convergent method. Moreover, this approach enables one to relax restrictions on the nonlinearity of the forward operator, as were used in previous work on regularization methods for nonlinear ill-posed problems.
引用
收藏
页码:637 / 665
页数:29
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