A parallel variant of BiCGStar-plus method reduced to single global synchronization

Abstract

In this paper, we propose new product-type iterative methods by introducing the BiCGSafe strategy, i.e., utilization of associate residual in place of residual, to the variants of GPBiCG. We refer to BiCGStar (BiCG with stabilization of associate residual) and its improved version of BiCGStar method. BiCGStar and BiCGStar-plus methods outperform compared with the conventional iterative methods. Moreover, our proposed methods are suited to parallel computer with distributed memory systems, since they require single global synchronization per one iteration. © Springer-Verlag Berlin Heidelberg 2013.