Kaczmarz methods for regularizing nonlinear ill-posed equations II: Applications

Markus Haltmeier; Richard Kowar; Antonio Leitão; Otmar Scherzer

doi:10.3934/ipi.2007.1.507

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2007, Volume 1, Issue 3: 507-523. Doi: 10.3934/ipi.2007.1.507

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Kaczmarz methods for regularizing nonlinear ill-posed equations II: Applications

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

Received: January 31, 2007

Published: July 2007

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Abstract

In part I we introduced modified Landweber--Kaczmarz methods and established a convergence analysis. In the present work we investigate three applications: an inverse problem related to thermoacoustic tomography, a nonlinear inverse problem for semiconductor equations, and a nonlinear problem in Schlieren tomography. Each application is considered in the framework established in the previous part. The novel algorithms show robustness, stability, computational efficiency and high accuracy.

Keywords:

Ill-posed systems; Landweber--Kaczmarz; Regularization.

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

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