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Stochastic Perturbation Theory

G. W. Stewart
SIAM Review
Vol. 32, No. 4 (Dec., 1990), pp. 579-610
Stable URL: http://www.jstor.org/stable/2030895
Page Count: 32
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Stochastic Perturbation Theory
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Abstract

In this paper classical matrix perturbation theory is approached from a probabilistic point of view. The perturbed quantity is approximated by a first-order perturbation expansion, in which the perturbation is assumed to be random. This permits the computation of statistics estimating the variation in the perturbed quantity. Up to the higher-order terms that are ignored in the expansion, these statistics tend to be more realistic than perturbation bounds obtained in terms of norms. The technique is applied to a number of problems in matrix perturbation theory, including least squares and the eigenvalue problem.

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