Global Simpler GMRES For Solving Nonsymmetric System With Multiple Right-hand Sides

Block GMRES is the most popular method for solving nonsymmetric linear systems with multiple right-hand sides. In practical applications, there exist a large variety of modifications to the standard block GMRES algorithm. Among these modifications, simpler block GMRES converts a least squares problem into a trian-gular matrix linear system, so it is less expensive than block GMRES. In this paper, we give a new method named global simpler GMRES, which is based on simpler block GMRES and is obtained by combining it with global Arnoldi. The main ad-vantage of our method is that less storage and computational work per restart cycle are required. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.