We study random eigenvalue problems in the context of spectral stochasticfinite elements. In particular, given a parameter-dependent, symmetricpositive-definite matrix operator, we explore the performance of algorithms forcomputing its eigenvalues and eigenvectors represented using polynomial chaosexpansions. We formulate a version of stochastic inverse subspace iteration,which is based on the stochastic Galerkin finite element method, and we compareits accuracy with that of Monte Carlo and stochastic collocation methods. Thecoefficients of the eigenvalue expansions are computed from a stochasticRayleigh quotient. Our approach allows the computation of interior eigenvaluesby deflation methods, and we can also compute the coefficients of multipleeigenvectors using a stochastic variant of the modified Gram-Schmidt process.The effectiveness of the methods is illustrated by numerical experiments onbenchmark problems arising from vibration analysis.
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