Regularization of systems of nonlinear ill-posed equations: I. Convergence Analysis

11/19/2020

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by   M. Haltmeier, et al.

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In this article we develop and analyze novel iterative regularization techniques for the solution of systems of nonlinear ill–posed operator equations. The basic idea consists in considering separately each equation of this system and incorporating a loping strategy. The first technique is a Kaczmarz-type method, equipped with a novel stopping criteria. The second method is obtained using an embedding strategy, and again a Kaczmarz-type approach. We prove well-posedness, stability and convergence of both methods.