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.

翻译：在本条中,我们开发并分析了解决非线性不良运算方程式系统的新迭代正规化技术,其基本理念是分别考虑这个系统的每个方程式,并纳入一个绕行战略。第一种技术是卡兹马兹型方法,配有新的停止标准。第二种方法是使用嵌入战略获得的,而另一种方法则是卡兹马尔兹型方法。我们证明这两种方法都有很好的定位、稳定性和趋同性。