论文标题
用于求解线性系统的贪婪的Motzkin-Kaczmarz方法
Greedy Motzkin-Kaczmarz methods for solving linear systems
论文作者
论文摘要
著名的贪婪随机Kaczmarz（GRK）方法在最大距离上使用贪婪的选择规则来确定工作行索引的子集。在本文中，使用最大残留的贪婪选择规则，我们提出了线性系统的贪婪随机Motzkin-Kaczmarz（GRMK）方法。还提供了新方法的块版。我们分析了两种方法的收敛性，并提供相应的收敛因子。广泛的数值实验表明，GRMK方法的性能几乎与GRK方法的密集矩阵方法相同，而前者在计算某些稀疏矩阵的计算时间方面表现更好，并且GRMK和GRK方法的块版本始终具有相同的性能。
The famous greedy randomized Kaczmarz (GRK) method uses the greedy selection rule on maximum distance to determine a subset of the indices of working rows. In this paper, with the greedy selection rule on maximum residual, we propose the greedy randomized Motzkin-Kaczmarz (GRMK) method for linear systems. The block version of the new method is also presented. We analyze the convergence of the two methods and provide the corresponding convergence factors. Extensive numerical experiments show that the GRMK method has almost the same performance as the GRK method for dense matrices and the former performs better in computing time for some sparse matrices, and the block versions of the GRMK and GRK methods always have almost the same performance.
