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

Johann Baumeister; Barbara Kaltenbacher; Antonio Leitão

doi:10.3934/ipi.2010.4.335

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2010, Volume 4, Issue 3: 335-350. Doi: 10.3934/ipi.2010.4.335

This issue Previous Article Next Article A quasi-reversibility approach to solve the inverse obstacle problem

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
2.
University of Graz, Institute for Mathematics and Scientific Computing, Heinrichstr. 36/III, A-8010 Graz
3.
Department of Mathematics, Federal University of St. Catarina, P.O. Box 476, 88040-900 Florianópolis

Received: June 30, 2009

Revised: September 30, 2009

Published: July 2010

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Abstract

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.

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Mathematics Subject Classification: Primary: 65J20; Secondary: 47J06.

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