强超松弛加速分布式Kaczmarz算法
Accelerating the Distributed Kaczmarz Algorithm by Strong Over-relaxation
摘要：
分布式Kaczmarz算法是标准Kaczmarz算法的一种适应，适用于数据分布在由树表示的整个网络中的情况。我们隔离子结构的网络和研究收敛性的分布式Kazmarz算法相对较大的松弛因子与这些子结构。如果系统是一致的，那么算法收敛到最小范数的解;然而，如果系统是不一致的，那么算法收敛到依赖于参数和网络拓扑的近似最小二乘解。我们发现，在这种情况下，松弛因子可能大于文献中的标准上限，并提供数值实验来支持我们的结果。
英文摘要：
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 Kazmarz 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
