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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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The Rayleigh quotient iteration and some generalizations for nonnormal matrices
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by B. N. Parlett PDF
Math. Comp. 28 (1974), 679-693 Request permission

Abstract:

The Rayleigh Quotient Iteration (RQI) was developed for real symmetric matrices. Its rapid local convergence is due to the stationarity of the Rayleigh Quotient at an eigenvector. Its excellent global properties are due to the monotonic decrease in the norms of the residuals. These facts are established for normal matrices. Both properties fail for nonnormal matrices and no generalization of the iteration has recaptured both of them. We examine methods which employ either one or the other of them.
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Math. Comp. 28 (1974), 679-693
  • MSC: Primary 65F15
  • DOI: https://doi.org/10.1090/S0025-5718-1974-0405823-3
  • MathSciNet review: 0405823