Accelerating the distributed Kaczmarz algorithm by strong over-relaxation
Accelerating the distributed Kaczmarz algorithm by strong over-relaxation
复制标题
通过强过度松弛加速分布式 Kaczmarz 算法
DOI：
10.1016/j.laa.2020.10.035
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发表时间：
2021
影响因子：
1.1
通讯作者：
Weber, Eric S.
中科院分区：
文献类型：
--
作者：
Borgard, Riley;Harding, Steven N.;Duba, Haley;Makdad, Chloe;Mayfield, Jay;Tuggle, Randal;Weber, Eric S.
分布式Kaczmarz算法是对标准Kaczmarz算法的一种改进，以适应数据在用树表示的网络中分布的情况。我们分离了网络的子结构，并研究了与这些子结构相关的相对大的松弛参数下分布式Kaczmarz算法的收敛性。如果系统是一致的，则算法收敛于最小范数的解；然而，如果系统不一致，则算法收敛到依赖于参数和网络拓扑的近似最小二乘解。在此背景下，我们证明了文献中的松弛参数可能大于标准上界，并提供了数值实验来支持我们的结果。
The distributed Kaczmarz algorithm is an adaptation of the standard Kaczmarz algorithm to the situation in which data is distributed throughout a network represented by a tree. We isolate substructures of the network and study convergence of the distributed Kaczmarz algorithm for relatively large relaxation parameters associated to these substructures. If the system is consistent, then the algorithm converges to the solution of minimal norm; however, if the system is inconsistent, then the algorithm converges to an approximated least-squares solution that is dependent on the parameters and the network topology. We show that the relaxation parameters may be larger than the standard upper-bound in literature in this context and provide numerical experiments to support our results.