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

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.
Citation: Johann Baumeister, Barbara Kaltenbacher, Antonio Leitão. On Levenberg-Marquardt-Kaczmarz iterative methods for solving systems of nonlinear ill-posed equations. Inverse Problems & Imaging, 2010, 4 (3) : 335-350. doi: 10.3934/ipi.2010.4.335
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