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.
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
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