To solve nonlinear problems, we construct two kinds of greedy capped nonlinear Kaczmarz methods by setting a capped threshold and introducing an effective probability criterion for selecting a row of the Jacobian matrix. The capped threshold and probability criterion are mainly determined by the maximum residual and maximum distance rules. The block versions of the new methods are also presented. We provide the convergence analysis of these methods and their numerical results behave quite well.

翻译：为了解决非线性问题,我们通过设定上限阈值和引入选择雅各克矩阵一行的有效概率标准,构建了两种贪婪的峰值非线性卡茨马尔兹(Kaczmarz)方法。上限阈值和概率标准主要由最大剩余和最大距离规则决定。还介绍了新方法的轮挡版本。我们提供了这些方法的趋同分析及其数字结果表现良好。