论文标题
非线性不良方程系统的正则化：I。收敛分析
Regularization of systems of nonlinear ill-posed equations: I. Convergence Analysis
论文作者
论文摘要
在本文中，我们为非线性不良操作员方程系统的解决方案开发和分析了新型的迭代正则化技术。基本思想在于分别考虑该系统的每个方程式并结合了倾斜策略。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，并再次获得Kaczmarz型方法。我们证明了两种方法的适当性，稳定性和收敛性。
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.
