Abstract. The GMRES method for solving nonsymmetric linear equations is generally used with restarting to reduce storage and orthogonalization costs. Restarting slows down the convergence. However, it is possible to save some important information at the time of the restart. It is proposed that approximate eigenvectors corresponding to a few of the smallest eigenvalues be formed and added to the subspace for GMRES. The convergence can be much faster, and the minimum residual property is retained.
Our GMRES implementation adds approximate eigenvectors corresponding to a few smallest eigenvalues of the matrix to the subspace in order to mitigate the impact of restarting on convergence REF .
A restarted GMRES method augmented with eigenvectors
SIAM J. Matrix Anal. Appl
Computer Science Mathematics