Recently, a new variant of the BiCGStab method, known as the pipeline BiCGStab, has been proposed. This method can achieve a higher degree of scalability and speed-up rates through a mechanism in which the communication phase for the computation of the inner product can be overlapped with the computation of the matrix-vector product. On the other hand, there exist several generalized iteration methods with better convergence behavior than BiCGStab such as ssBiCGSafe, BiCGSafe, GPBi-CG. Of these methods, ssBiCGSafe, which requires a single phase of computing inner products per one iteration, is best suited for high-performance computing systems. In this paper, inspired by the success of the pipelined BiCGStab method, we propose variations of the ssBiCGSafe method, in which only one phase of inner product computation per iteration is required and this inner product computation phase can be overlapped with the matrix-vector computation. Through numerical experiments, we show that the proposed methods lead to improvements in convergence behavior and execution time compared to the pipelined BiCGStab and ssBiCGSafe methods.

翻译：最近,提出了称为管道BiCGStab的BiCGStab方法的新变体,该方法可以通过一种机制实现更高程度的可缩放性和加速率,即内部产品计算通信阶段可以与矩阵-矢量器产品的计算重叠;另一方面,存在一些通用的循环法,其趋同行为比比BiCGStab方法(例如SsBiCGSafe,BiCGSafe,GPBI-CG)。在这些方法中,SsBiCGSafe(每循环一次计算内部产品需要单一阶段的计算)最适合于高性能的计算系统。在本文中,由于管道BiCGStab方法的成功,我们建议对SBiCGSafe方法进行修改,其中只要求每循环计算一个内部产品计算阶段,而这一内部产品计算阶段可以与矩阵-矢量计算重叠。我们通过数字实验,表明拟议的方法可以改进聚合行为和执行时间,与管道BiGSC方法相比较。