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Iterative solution of the random eigenvalue problem with application to spectral stochastic finite element systems
Author(s) -
Verhoosel C. V.,
Gutiérrez M. A.,
Hulshoff S. J.
Publication year - 2006
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1712
Subject(s) - eigenvalues and eigenvectors , mathematics , inverse iteration , discretization , computation , eigenvalue perturbation , power iteration , convergence (economics) , finite element method , inverse , random matrix , matrix (chemical analysis) , iterative method , mathematical analysis , mathematical optimization , algorithm , geometry , physics , materials science , quantum mechanics , economics , composite material , thermodynamics , economic growth
A new algorithm for the computation of the spectral expansion of the eigenvalues and eigenvectors of a random non‐symmetric matrix is proposed. The algorithm extends the deterministic inverse power method using a spectral discretization approach. The convergence and accuracy of the algorithm is studied for both symmetric and non‐symmetric matrices. The method turns out to be efficient and robust compared to existing methods for the computation of the spectral expansion of random eigenvalues and eigenvectors. Copyright © 2006 John Wiley & Sons, Ltd.