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REVIEW ARTICLES

Eigenvalue Problem for Uncertain Systems

[+] Author and Article Information
Mircea Grigoriu

Cornell University, Ithaca NY 14853

Appl. Mech. Rev 44(11S), S89-S95 (Nov 01, 1991) doi:10.1115/1.3121377 History: Online April 30, 2009

Abstract

Methods are developed for calculating probabilistic characteristics of the eigenvalues of stochastic symmetric matrices. The methods are based on the relationship between the elements of a matrix and its eigenvalues, perturbation method, bounds on eigenvalues, and zero-crossings of the characteristic polynomial. It is shown that the polynomial characteristic of a stochastic matrix can be viewed as a random process whose crossings of level zero define the eigenvalues of the matrix. The proposed methods of analysis are demonstrated by examples from dynamics and elasticity.

Copyright © 1991 by American Society of Mechanical Engineers
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