Geodesic
New filtering strategies for implicitly restarted Lanczos iteration
Electronic transactions on numerical analysis, Tome 45 (2016), pp. 16-32.

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Summary: Implicitly-restarted Lanczos iteration methods are among the most powerful methods for finding a small number of eigenpairs of Hermitian matrices. These methods enjoy strong convergence and have manageable memory requirements. Implicitly-restarted Lanczos methods naturally find approximations to both the largest and smallest eigenpairs of the input matrix, but stagnation of Ritz values may lead to slow convergence, especially when one only wants eigenvalues from one end of the spectrum and memory is constrained. We develop a filtering strategy that breaks Ritz value stagnation for these one-sided eigenvalue problems. We demonstrate the reduction in matrix-vector product costs and note that this new variant has marked advantages when memory is constrained and when matrix-vector products are expensive.
Classification : 65F15, 15A18, 90C99
Keywords: implicitly-restarted Lanczos, polynomial filtering, Hermitian eigenvalue problems, Krylov subspaces, Chebyshev filtering 
@article{ETNA_2016__45__a24,
     author = {Breuer, Alex},
     title = {New filtering strategies for implicitly restarted {Lanczos} iteration},
     journal = {Electronic transactions on numerical analysis},
     pages = {16--32},
     publisher = {mathdoc},
     volume = {45},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2016__45__a24/}
}
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Breuer, Alex. New filtering strategies for implicitly restarted Lanczos iteration. Electronic transactions on numerical analysis, Tome 45 (2016), pp. 16-32. http://geodesic.mathdoc.fr/item/ETNA_2016__45__a24/