论文标题
基于双分裂的交替固定迭代方法
Alternating Stationary Iterative Methods Based on Double Splittings
论文作者
论文摘要
矩阵双重迭代迭代在实现方面很简单，同时求解了真实的非单独（矩形）线性系统。在本文中，我们提出了两个通过两个双分裂制定的交替双重分裂（AD）方案，然后交替进行各自的迭代。然后讨论收敛条件以及比较分析。每个ADS方案中使用的双重分组集诱导了一个预处理系统，有助于显示ADS方案的收敛性。我们还表明，一个广告方案的矩阵类别比另一个广告方案更好。数值实验证实了所提出的ADS方案优于实际实施中现有的方法。 Though the problems are considered in the rectangular matrix settings, the same problems are even new in non-singular matrix settings.
Matrix double splitting iterations are simple in implementation while solving real non-singular (rectangular) linear systems. In this paper, we present two Alternating Double Splitting (ADS) schemes formulated by two double splittings and then alternating the respective iterations. The convergence conditions are then discussed along with comparative analysis. The set of double splittings used in each ADS schemes induce a preconditioned system which helps in showing the convergence of the ADS schemes. We also show that the classes of matrices for which one ADS scheme is better than the other are mutually exclusive. Numerical experiments confirm the proposed ADS schemes are superior to the existing methods in actual implementation. Though the problems are considered in the rectangular matrix settings, the same problems are even new in non-singular matrix settings.
