# American Institute of Mathematical Sciences

February  2014, 8(1): 149-172. doi: 10.3934/ipi.2014.8.149

## Convergence rates for Kaczmarz-type regularization methods

 1 Industrial Mathematics Institute, Johannes Kepler University Linz, A-4040 Linz 2 Department of Mathematics, Federal University of St. Catarina, P.O. Box 476, 88040-900 Florianópolis

Received  August 2012 Revised  November 2013 Published  March 2014

This article is devoted to the convergence analysis of a special family of iterative regularization methods for solving systems of ill--posed operator equations in Hilbert spaces, namely Kaczmarz-type methods. The analysis is focused on the Landweber--Kaczmarz (LK) explicit iteration and the iterated Tikhonov--Kaczmarz (iTK) implicit iteration. The corresponding symmetric versions of these iterative methods are also investigated (sLK and siTK). We prove convergence rates for the four methods above, extending and complementing the convergence analysis established originally in [22,13,12,8].
Citation: Stefan Kindermann, Antonio Leitão. Convergence rates for Kaczmarz-type regularization methods. Inverse Problems & Imaging, 2014, 8 (1) : 149-172. doi: 10.3934/ipi.2014.8.149
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