English

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

Numerical Analysis 2020-11-20 v1 Numerical Analysis

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.

Keywords

Cite

@article{arxiv.2011.09893,
  title  = {Regularization of systems of nonlinear ill-posed equations: I. Convergence Analysis},
  author = {M. Haltmeier and A. Leitao and O. Scherzer},
  journal= {arXiv preprint arXiv:2011.09893},
  year   = {2020}
}

Comments

11 pages, 1 figure

R2 v1 2026-06-23T20:22:23.575Z