Numerical Algorithms

, Volume 60, Issue 2, pp 279–295

Strategies for spectrum slicing based on restarted Lanczos methods

Original Paper

DOI: 10.1007/s11075-012-9564-z

Cite this article as:
Campos, C. & Roman, J.E. Numer Algor (2012) 60: 279. doi:10.1007/s11075-012-9564-z

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.

Keywords

Large-scale eigenvalue computations Spectrum slicing Parallel numerical libraries 

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.D. Sistemes Informàtics i ComputacióUniversitat Politècnica de ValènciaValènciaSpain