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February 2011, 5(1): 1-17. doi: 10.3934/ipi.2011.5.1
Modified iterated Tikhonov methods for solving systems of nonlinear ill-posed equations
Adriano De Cezaro 1, , Johann Baumeister 2, and Antonio Leitão 3,
Institute of Mathematics Statistics and Physics, Federal University of Rio Grande, Av. Italia km 8, 96201-900 Rio Grande, Brazil
Fachbereich Mathematik, Johann Wolfgang Goethe Universität, Robert–Mayer–Str. 6–10, 60054 Frankfurt am Main
Department of Mathematics, Federal University of St. Catarina, P.O. Box 476, 88040-900 Florianópolis
Received October 2009 Revised September 2010 Published February 2011
We investigate iterated Tikhonov methods coupled with a Kaczmarz strategy for obtaining stable solutions of nonlinear systems of ill-posed operator equations. We show that the proposed method is a convergent regularization method. In the case of noisy data we propose a modification, the so called loping iterated Tikhonov-Kaczmarz method, where a sequence of relaxation parameters is introduced and a different stopping rule is used. Convergence analysis for this method is also provided.
Keywords: Ill-posed equations, iterated Tikhonov method, Nonlinear systems, Regularization, Kaczmarz method..
Mathematics Subject Classification: Primary: 65J20; Secondary: 47J0.
Citation: Adriano De Cezaro, Johann Baumeister, Antonio Leitão. Modified iterated Tikhonov methods for solving systems of nonlinear ill-posed equations. Inverse Problems & Imaging, 2011, 5 (1) : 1-17. doi: 10.3934/ipi.2011.5.1
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Adriano De Cezaro Johann Baumeister Antonio Leitão