We investigate iterated Tikhonov methods coupled with a Kaczmarz strategy for obtaining stable solutions of nonlinear systems of ill-posed operator equations. We show that the proposed method is a convergent regularization method. In the case of noisy data we propose a modification, the so called loping iterated Tikhonov-Kaczmarz method, where a sequence of relaxation parameters is introduced and a different stopping rule is used. Convergence analysis for this method is also provided.

翻译：我们调查了迭代的Tikhonov 方法以及卡茨马尔兹战略,以找到稳定办法解决非线性操作器等式的非线性系统。我们表明,拟议方法是一种趋同的正规化方法。对于吵闹的数据,我们提议修改,即所谓的斜斜变的Tikhonov-Kaczmarz方法,在这种方法中引入了放松参数序列,并使用了不同的停止规则。我们还提供了该方法的一致分析。