论文标题
贪婪的随机抽样非线性kaczmarz方法
Greedy randomized sampling nonlinear Kaczmarz methods
论文作者
论文摘要
最近提出了非线性kaczmarz方法来求解非线性方程系统。在本文中，我们首先讨论了非线性kaczmarz迭代的两个贪婪选择规则，即最大残差和最大距离规则。然后，基于它们，提出了两种贪婪的随机抽样方法。此外，我们还设计了四个相应的贪婪随机块方法，即基于多个样本的方法。证明了所有提出的方法的期望中的线性收敛。数值结果表明，在某些应用程序中，包括棕色几乎线性函数和广义线性模型，贪婪的选择规则比随机的收敛速率更快，而块方法的表现优于单个样本的融合率。
The nonlinear Kaczmarz method was recently proposed to solve the system of nonlinear equations. In this paper, we first discuss two greedy selection rules, i.e., the maximum residual and maximum distance rules, for the nonlinear Kaczmarz iteration. Then, based on them, two kinds of greedy randomized sampling methods are presented. Further, we also devise four corresponding greedy randomized block methods, i.e., the multiple samples-based methods. The linear convergence in expectation of all the proposed methods is proved. Numerical results show that, in some applications including brown almost linear function and generalized linear model, the greedy selection rules give faster convergence rates than the random ones, and the block methods outperform the single sample-based ones.
