Abstract
Frommer and Glassner [Frommer, A. and Glassner, U., 1998, Restarted GMRES for shifted linear systems, SIAM Journal on Scientific Computing, 19, 15–26.] develop a variant of the restarted GMRES method for shifted linear systems at the expense of only one matrix–vector multiplication per iteration. However, restarting slows down the convergence, even stagnation. We present a variant of the restarted GMRES augmented with some approximate eigenvectors for the shifted systems. The convergence can be much faster at little extra expense. Numerical experiments show its efficiency.
Acknowledgements
Supported by the National Natural Science Foundation of China (10271075) and the Science and Technology Developing Foundation of University in Shanghai of China (02AK41).