A Lanczos-type method for solving nonsymmetric linear systems with multiple right-hand sides — matrix and polynomial interpretation

In this paper, we propose a method with a finite termination property for solving the linear system AX = B where A is a nonsymmetric complex n×n matrix and B is an arbitrary n×s rectangular matrix. s does not have to be small. The method is based on a single Krylov subspace where all the systems are picking informations. A polynomial and a single matrix interpretation is given which seems to be new from a theoretical point of view. Numerical experiments show that the convergence is usually quite good even if s is relatively large. The memory requirements and the computational costs seem to be interesting too.