Strategies for spectrum slicing based on restarted Lanczos methods |
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Authors: | Carmen Campos Jose E Roman |
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Institution: | 1.D. Sistemes Informàtics i Computació,Universitat Politècnica de València,València,Spain |
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Abstract: | In the context of symmetric-definite generalized eigenvalue problems, it is often required to compute all eigenvalues contained
in a prescribed interval. For large-scale problems, the method of choice is the so-called spectrum slicing technique: a shift-and-invert
Lanczos method combined with a dynamic shift selection that sweeps the interval in a smart way. This kind of strategies were
proposed initially in the context of unrestarted Lanczos methods, back in the 1990’s. We propose variations that try to incorporate
recent developments in the field of Krylov methods, including thick restarting in the Lanczos solver and a rational Krylov
update when moving from one shift to the next. We discuss a parallel implementation in the SLEPc library and provide performance
results. |
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Keywords: | |
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