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.

中文翻译：

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非线性不适定方程组的正则化：一、收敛分析

在本文中，我们开发并分析了用于求解非线性不适定算子方程组的新颖迭代正则化技术。基本思想在于分别考虑该系统的每个方程并结合一个循环策略。第一种技术是 Kaczmarz 型方法，配备了新的停止标准。第二种方法是使用嵌入策略获得的，也是 Kaczmarz 类型的方法。我们证明了两种方法的适定性、稳定性和收敛性。