GPMR: An Iterative Method for Unsymmetric Partitioned Linear Systems
Alexis Montoison, Dominique Orban · SIAM Journal on Matrix Analysis and Applications · 2023
Abstract. We introduce an iterative method named Gpmr (general partitioned minimum residual) for solving [Formula: see text] block unsymmetric linear systems. Gpmr is based on a new process that simultaneously reduces two rectangular matrices to upper Hessenberg form and is closely related to the block-Arnoldi process. Gpmr is tantamount to Block-Gmres with two right-hand sides in which the two approximate solutions are summed at each iteration, but its storage and work per iteration are similar to those of Gmres. We compare the performance of Gpmr with Gmres on linear systems from the SuiteSparse Matrix Collection. In our experiments, Gpmr terminates significantly earlier than Gmres on a residual-based stopping condition with an improvement ranging from around 10% up to 50% in terms of number of iterations.