论文标题
通过强弹性过度释放加速分布式的kaczmarz算法
Accelerating the Distributed Kaczmarz Algorithm by Strong Over-relaxation
论文作者
论文摘要
分布式的Kaczmarz算法是标准Kaczmarz算法对数据分布在由树代表的网络中分布到的情况的情况。我们分离网络的子结构，并研究分布式Kazmarz算法的收敛性，以实现与这些子结构相关的相对较大的松弛参数。如果系统一致，则算法会收敛到最小规范的解决方案。但是，如果系统不一致，则算法将收敛到依赖于参数和网络拓扑的近似最小二乘解决方案。我们表明，在这种情况下，放松参数可能大于文献中的标准上限，并提供数值实验以支持我们的结果。
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 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.
