An improved bi-conjugate residual algorithm suitable for distributed parallel computing

An improved bi-conjugate residual (BiCR) method (IBiCR method, in brief) for solving large sparse linear systems with unsymmetrical coefficient matrices was proposed for distributed parallel environments. The method reduced two global synchronization points to one by reconstructing BiCR method and all inner products per iteration were independent and communication time required for inner product can be overlapped efficiently with computation time of vector updates. It combines the elements of numerical stability with the characters of design of parallel algorithms. The cost is only a little increased computation. Performance and isoefficiency analysis shows that IBiCR method has better parallelism and scalability than BiCR method. Numerical experiments show that the parallel performance can be improved by a factor of about 2. We compared also IBiCR with IBiCG and BiCR with BiCG methods. The results show that BiCR and IBiCR methods convergent at the same number of iteration, and they convergent faster than BiCG and IBiCG methods, respectively. Furthermore, IBiCR method conquers the vibration of residual norm of IBiCG method.