Modified iterated Tikhonov methods for solving systems of nonlinear
Adriano De Cezaro - Institute of Mathematics Statistics and Physics, Federal University of Rio Grande, Av. Italia km 8, 96201-900 Rio Grande, Brazil (email)
Abstract: 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: Nonlinear systems, Ill-posed equations, Regularization,
iterated Tikhonov method, Kaczmarz method.
Received: October 2009; Revised: September 2010; Published: February 2011.
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