中文摘要：

A modified GMRES method is proposed in this paper, the method replaces the approximation xm obtained by the GMRES method with a new approximation xm which is a linear combination of xm and the wasted basis vector vm+1. The residual norm of the new approximation satisfies a small one-dimensional minimization problem. Relationships between the residual norms of xm and xm are given. We show that the resulting m-step modified GMRES method is better than the original m-step GMRES method in theory and is consi...

英文摘要：

A modified GMRES method is proposed in this paper, the method replaces the approximation xm obtained by the GMRES method with a new approximation xm which is a linear combination of xm and the wasted basis vector vm+1. The residual norm of the new approximation satisfies a small one-dimensional minimization problem. Relationships between the residual norms of xm and xm are given. We show that the resulting m-step modified GMRES method is better than the original m-step GMRES method in theory and is consider...