Regularizing Newton-Kaczmarz Methods for Nonlinear Ill-Posed Problems
Regularizing Newton-Kaczmarz Methods for Nonlinear Ill-Posed Problems
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DOI：
10.1137/040613779
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发表时间：
2006-01
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影响因子：
--
通讯作者：
M. Burger;B. Kaltenbacher
中科院分区：
文献类型：
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作者：
M. Burger;B. Kaltenbacher
我们引入了一类用于非线性病态问题的镇定Newton-Kaczmarz方法，并分析了它们的收敛性和正则化行为。与求解非线性不适定问题的迭代方法一样，必须施加非线性（或导数）条件才能获得收敛。正如我们将在一般情况下和在一些具体示例中讨论的那样，Newton-Kaczmarz 方法获得的非线性条件比先前存在的迭代方法的限制更少，并且可以针对多个实际应用进行验证。我们还讨论了Newton-Kaczmarz方法每一步中出现的线性问题的离散化和高效数值求解，并对两个模型问题进行了数值实验。
We introduce a class of stabilizing Newton--Kaczmarz methods for nonlinear ill-posed problems and analyze their convergence and regularization behavior. As usual for iterative methods for solving nonlinear ill-posed problems, conditions on the nonlinearity (or the derivatives) have to be imposed in order to obtain convergence. As we shall discuss in general and in some specific examples, the nonlinearity conditions obtained for the Newton--Kaczmarz methods are less restrictive than those for previously existing iteration methods and can be verified for several practical applications. We also discuss the discretization and efficient numerical solution of the linear problems arising in each step of a Newton--Kaczmarz method, and we carry out numerical experiments for two model problems.