Restarted Gmres Augmented With Eigenvectors For Shifted Linear Systems * Supported by the National Natural Science Foundation of China and the Science and Technology Developing Foundation of University in Shanghai of China

Shifted matrices, which differ by a multiple of the identity only, generate the same Krylov subspaces with respect to any fixed vector. Frommer and Glassner [5] develop a variant of the restarted GMRES method for such shifted 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 eigenvectors for the shifted systems. The convergence can be much faster at little extra expense. Numerical experiments show its efficiency.

Keywords:

• Shifted Systems
• Augmented Gmres Method
• Restarting