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Strategies for spectrum slicing based on restarted Lanczos methods

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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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Authors and Affiliations

  1. D. Sistemes Informàtics i Computació, Universitat Politècnica de València, Camí de Vera s/n, 46022, València, Spain

    Carmen Campos & Jose E. Roman

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  1. Carmen Campos
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  2. Jose E. Roman
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Correspondence to Jose E. Roman.

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This work was supported by the Spanish Ministerio de Ciencia e Innovación under grant TIN2009-07519.

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Campos, C., Roman, J.E. Strategies for spectrum slicing based on restarted Lanczos methods. Numer Algor 60, 279–295 (2012). https://doi.org/10.1007/s11075-012-9564-z

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