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August  2010, 4(3): 335-350. doi: 10.3934/ipi.2010.4.335

On Levenberg-Marquardt-Kaczmarz iterative methods for solving systems of nonlinear ill-posed equations

Johann Baumeister 1, , Barbara Kaltenbacher 2, and  Antonio Leitão 3,

1. 

Fachbereich Mathematik, Johann Wolfgang Goethe Universität, Robert–Mayer–Str. 6–10, 60054 Frankfurt am Main, Germany
2. 

University of Graz, Institute for Mathematics and Scientific Computing, Heinrichstr. 36/III, A-8010 Graz, Austria
3. 

Department of Mathematics, Federal University of St. Catarina, P.O. Box 476, 88040-900 Florianópolis, Brazil

Received  July 2009 Revised  October 2009 Published  July 2010

In this article a modified Levenberg-Marquardt method coupled with a Kaczmarz strategy for obtaining stable solutions of nonlinear systems of ill-posed operator equations is investigated. We show that the proposed method is a convergent regularization method. Numerical tests are presented for a non-linear inverse doping problem based on a bipolar model.
Keywords: Kaczmarz method., Levenberg-Marquardt method, Regularization, Nonlinear systems, Ill-posed equations.
Mathematics Subject Classification: Primary: 65J20; Secondary: 47J0.
Citation: Johann Baumeister, Barbara Kaltenbacher, Antonio Leitão. On Levenberg-Marquardt-Kaczmarz iterative methods for solving systems of nonlinear ill-posed equations. Inverse Problems and Imaging, 2010, 4 (3) : 335-350. doi: 10.3934/ipi.2010.4.335
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