A shifted block Lanczos algorithm for solving sparse symmetric generalized eigenproblems. (English) Zbl 0803.65044

Authors’ summary: An “industrial strength” algorithm for solving sparse symmetric generalized eigenproblems is described. The algorithm has its foundations in known techniques in solving sparse symmetric eigenproblems, notably the spectral transformation of T. Ericsson and A. Ruhe [Math. Comput. 35, 1251-1268 (1980; Zbl 0468.65021)] and the block Lanczos algorithm. However, the combination of these two techniques is not trivial; there are many pitfalls awaiting the unwary implementor.
The focus of this paper is on identifying those pitfalls and avoiding them, leading to a “bomb-proof” algorithm that can live as a black box eigensolver inside a large applications code. The code that results comprises a robust shift selection strategy and a block Lanczos algorithm that is a novel combination of new techniques and extensions of old techniques.


65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65F50 Computational methods for sparse matrices


Zbl 0468.65021
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