An improved generalized conjugate residual squared (IGCRS2) algorithm suitable for distributed parallel computing

In this paper, based on generalized conjugate residual squared (GCRS2) algorithm in Zhang et al. (2010 Third International Conference on Information and Computing, pp 326–329, 2010) and the ideas in Gu et al. (Appl Math Comput 186:1243–1253, 2007), we present an improved generalized conjugate residual squared (IGCRS2) algorithm, which is designed for distributed parallel environments. The improved algorithm reduces two global synchronization points to one by changing the computation sequence in the GCRS2 algorithm and all inner products per iteration are independent and communication time required for inner product can be overlapped with useful computation. Theoretical analysis and numerical comparison about isoefficiency analysis show that the IGCRS2 method has better parallelism and scalability than the GCRS2 method and the parallel performance can be improved by a factor of about 2.