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Regularization of systems of nonlinear ill-posed equations: I. Convergence Analysis (2011.09893v1)
Published 19 Nov 2020 in math.NA and cs.NA
Abstract: 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.