In this article, we propose an accuracy-assuring technique for finding a solution for unsymmetric linear systems. Such problems are related to different areas such as image processing, computer vision, and computational fluid dynamics. Parallel implementation of Krylov subspace methods speeds up finding approximate solutions for linear systems. In this context, the refined approach in pipelined BiCGStab enhances scalability on distributed memory machines, yielding to substantial speed improvements compared to the standard BiCGStab method. However, it's worth noting that the pipelined BiCGStab algorithm sacrifices some accuracy, which is stabilized with the residual replacement technique. This paper aims to address this issue by employing the ExBLAS-based reproducible approach. We validate the idea on a set of matrices from the SuiteSparse Matrix Collection.

翻译：本文提出一种用于求解非对称线性系统的精度保证技术。此类问题涉及图像处理、计算机视觉和计算流体力学等不同领域。Krylov子空间方法的并行实现可加速求解线性系统的近似解。在此背景下，改进后的流水线BiCGStab方法增强了分布式内存机器上的可扩展性，与标准BiCGStab方法相比，带来了显著的速度提升。然而，值得指出的是，流水线BiCGStab算法牺牲了一定的精度，而残差替换技术可使其稳定性得到改善。本文旨在通过采用基于ExBLAS的可复现方法解决这一问题。我们在SuiteSparse矩阵集合中的一组矩阵上验证了该设想。