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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

Estimating the largest eigenvalue of a positive definite matrix


Authors: Dianne P. O'Leary, G. W. Stewart and James S. Vandergraft
Journal: Math. Comp. 33 (1979), 1289-1292
MSC: Primary 65F15
MathSciNet review: 537973
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Abstract: The power method for computing the dominant eigenvector of a positive definite matrix will converge slowly when the dominant eigenvalue is poorly separated from the next largest eigenvalue. In this note it is shown that in spite of this slow convergence, the Rayleigh quotient will often give a good approximation to the dominant eigenvalue after a very few iterations-even when the order of the matrix is large.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1979-0537973-X
PII: S 0025-5718(1979)0537973-X
Article copyright: © Copyright 1979 American Mathematical Society