GPMR: An Iterative Method for Unsymmetric Partitioned Linear Systems

We introduce an iterative method named Gpmr (general partitioned minimum residual) for solving block unsymmetric linear systems. is based on a new process that simultaneously reduces two rectangular matrices to upper Hessenberg form and closely related the block-Arnoldi process. tantamount Block-Gmres with right-hand sides in which approximate solutions are summed at each iteration, but its storage work per iteration similar those of Gmres. compare performance Gmres systems from SuiteSparse Matrix Collection. In our experiments, terminates significantly earlier than residual-based stopping condition improvement ranging around 10% up 50% terms number iterations.