Modified iterated Tikhonov methods for solving systems of nonlinear ill-posed equations

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.

18 pages. arXiv admin note: text overlap with arXiv:0801.3088, arXiv:2011.09674

References in corpus (2)

• Regularization of systems of nonlinear ill-posed equations: I. Convergence Analysis
• On Levenberg-Marquardt-Kaczmarz iterative methods for solving systems of nonlinear ill-posed equations