Global GMRES with Deflated Restarting for Families of Shifted Linear Systems
Many problems in science and engineering field require the solution of shifted linear systems with multiple right hand sides and multiple shifts. To solve such systems efficiently, the implicitly restarted global GMRES algorithm is extended in this paper. However, the shift invariant property could no longer hold over the augmented global Krylov subspace due to adding the harmonic Ritz matrices. To remedy this situation, we enforce the collinearity condition on the shifted system and propose shift implicitly restarted global GMRES. The new method not only improves the convergence but also has a potential to simultaneously compute approximate solution for the shifted systems using only as many matrix vector multiplications as the solution of the seed system requires. In addition, some numerical experiments also confirm the effectiveness of our method.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1097489Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1606
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