# American Institute of Mathematical Sciences

May  2007, 1(2): 289-298. doi: 10.3934/ipi.2007.1.289

## Kaczmarz methods for regularizing nonlinear ill-posed equations I: convergence analysis

 1 Department of Computer Science,University of Innsbruck, Technikerstrasse 21a, A-6020 Innsbruck, Austria, Austria 2 Department of Mathematics, Federal University of St. Catarina, P.O. Box 476, 88040-900 Florianópolis, Brazil

Received  January 2007 Published  April 2007

In this article we develop and analyze novel iterative regularization techniques for the solution of systems of nonlinear ill-posed operator equations. The basic idea consists in considering separately each equation of this system and incorporating a loping strategy. The first technique is a Kaczmarz-type method, equipped with a novel stopping criteria. The second method is obtained using an embedding strategy, and again a Kaczmarz-type approach. We prove well-posedness, stability and convergence of both methods.
Citation: Markus Haltmeier, Antonio Leitão, Otmar Scherzer. Kaczmarz methods for regularizing nonlinear ill-posed equations I: convergence analysis. Inverse Problems and Imaging, 2007, 1 (2) : 289-298. doi: 10.3934/ipi.2007.1.289
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