Convergence rates for Kaczmarz-type regularization methods

Stefan Kindermann; Antonio Leitão

doi:10.3934/ipi.2014.8.149

Article Contents

2014, Volume 8, Issue 1: 149-172. Doi: 10.3934/ipi.2014.8.149

This issue Previous Article Adaptive meshing approach to identification of cracks with electrical impedance tomography Next Article Geometric reconstruction in bioluminescence tomography

Convergence rates for Kaczmarz-type regularization methods

Stefan Kindermann^1, and
Antonio Leitão^2,

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: February 2014

Abstract / Introduction Related Papers Cited by

Abstract

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].

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Mathematics Subject Classification: Primary: 65J20, 65J15; Secondary: 47J06.

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