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A Krylov–Schur algorithm for large eigenproblems. (English) Zbl 1003.65045
SIAM J. Matrix Anal. Appl. 23, No. 3, 601-614 (2002); addendum ibid. 24, No. 2, 599-601 (2002).
This paper removes two drawbacks of D. C. Sorensen’s implicitly restarted Arnoldi algorithm [ibid. 13, No. 1, 357-385 (1992; Zbl 0763.65025)] for finding a few eigenpairs of a large matrix (implemented in the ARPACK package of 1998). The drawbacks are (1) the restriction of possible transformations on the decompositions caused by the need to preserve the structure of the Arnoldi decomposition, and (2) the potential forward instability of the implicit QR-algorithm causing unwanted Ritz vectors to persist in the computation. For that purpose the paper introduces a general Krylov decomposition and solves the purging and deflating problems by relaxing the definition of an Arnoldi decomposition.

MSC:
65F50 Computational methods for sparse matrices
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
Software:
ARPACK; JDQR; JDQZ; TRLan
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