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 scheme induces 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 that the proposed ADS schemes have several computational advantages over the existing methods. Though the problems are considered in the rectangular matrix settings, the same problems are even new in non-singular matrix settings.

矩阵双分裂迭代易于实现，同时可以求解实际的非奇异（矩形）线性系统。在本文中，我们提出了两种交替两次拆分（ADS）方案，这些方案是通过两次双重拆分来制定的，然后交替进行各自的迭代。然后讨论收敛条件并进行比较分析。每个ADS方案中使用的一组双分裂诱导了一个预处理系统，该系统有助于显示ADS方案的收敛性。我们还表明，一种ADS方案优于另一种ADS方案的矩阵类别是互斥的。数值实验证实了所提出的ADS方案比现有方法具有更多的计算优势。尽管在矩形矩阵设置中考虑了这些问题，