On the block GMRES method with deflated restarting

In this paper, we consider the block-GMRES method with deflated restarting for solving nonsymmetric linear systems with multiple right-hand sides. We modify slightly the restarted block-GMRES method with deflation of eigenvalues proposed by Morgan to obtain a new one. It is shown that the modified method is mathematically equivalent to the Morgan’s original method. However, the error analysis shows the modified version minimizes the numerical errors during a restart and therefore is better suited if the linear systems have to be solved with high precision. Numerical experiments report the effectiveness of the modified method.