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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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The Lanczos algorithm with selective orthogonalization
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by B. N. Parlett and D. S. Scott PDF
Math. Comp. 33 (1979), 217-238 Request permission


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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Additional Information
  • © Copyright 1979 American Mathematical Society
  • Journal: Math. Comp. 33 (1979), 217-238
  • MSC: Primary 65F15
  • DOI:
  • MathSciNet review: 514820