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The Lanczos algorithm with selective orthogonalization

Authors: B. N. Parlett and D. S. Scott
Journal: Math. Comp. 33 (1979), 217-238
MSC: Primary 65F15
MathSciNet review: 514820
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Abstract: The simple Lanczos process is very effective for finding a few extreme eigenvalues of a large symmetric matrix along with the associated eigenvectors. Unfortunately, the process computes redundant copies of the outermost eigenvectors and has to be used with some skill. In this paper it is shown how a modification called selective orthogonalization stifles the formation of duplicate eigenvectors without increasing the cost of a Lanczos step significantly. The degree of linear independence among the Lanczos vectors is controlled without the costly process of reorthogonalization.

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Keywords: Eigenvalues, eigenvectors, symmetric matrices, Lanczos method
Article copyright: © Copyright 1979 American Mathematical Society