An improved generalized conjugate residual squared algorithm suitable for distributed parallel computing

In this paper, based on GCRS algorithm in Zhang and Zhao (2010) and the ideas in Gu et al. (2007), we present an improved generalized conjugate residual squared (IGCRS) algorithm that is designed for distributed parallel environments. The new improved algorithm reduces two global synchronization points to one by changing the computation sequence in the GCRS algorithm in such a way that all inner products per iteration are independent so that communication time required for inner products can be overlapped with useful computation. Theoretical analysis and numerical comparison of isoefficiency analysis show that the IGCRS method has better parallelism and scalability than the GCRS method, and the parallel performance can be improved by a factor of about 2. Finally, some numerical experiments clearly show that the IGCRS method can achieve better parallel performance with a higher scalability than the GCRS method and the improvement percentage of communication is up to 52.19% averagely, which meets our theoretical analysis.