The Rayleigh quotient iteration and some generalizations for nonnormal matrices-Reference-Cited by-同舟云学术

The Rayleigh quotient iteration and some generalizations for nonnormal matrices

Published:1974 Issue:127 Volume:28 Page:679-693
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Parlett B. N.

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1974-28-127/S0025-5718-1974-0405823-3/S0025-5718-1974-0405823-3.pdf

Reference13 articles.

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2. A generalized Rayleigh quotient iteration for lambda-matrices;Lancaster, P.;Arch. Rational Mech. Anal.,1961

3. On the convergence of the Rayleigh quotient iteration for the computation of the characteristic roots and vectors. I;Ostrowski, A. M.;Arch. Rational Mech. Anal.,1957

4. W. Kahan, Inclusion Theorems for Clusters of Eigenvalues of Hermitian Matrices, Technical Report, Dept. of Computer Sci., University of Toronto, 1967.

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