A periodic Krylov-Schur algorithm for large matrix products

Authors:
Daniel Kressner
Affiliations:
Department of Mathematics, , Bijenička 30, 10000, Zagreb, Croatia
Venue:
Numerische Mathematik
Year:
2006

Citing 0
Cited 3

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The Rayleigh-Ritz method, refinement and Arnoldi process for periodic matrix pairs

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On the Error in the Product QR Decomposition

SIAM Journal on Matrix Analysis and Applications

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Abstract

Stewart's recently introduced Krylov-Schur algorithm is a modification of the implicitly restarted Arnoldi algorithm which employs reordered Schur decompositions to perform restarts and deflations in a numerically reliable manner. This paper describes a variant of the Krylov-Schur algorithm suitable for addressing eigenvalue problems associated with products of large and sparse matrices. It performs restarts and deflations via reordered periodic Schur decompositions and, by taking the product structure into account, it is capable of achieving qualitatively better approximations to eigenvalues of small magnitude.