# Asymptotic convergence of spectral inverse iterations for stochastic eigenvalue problems

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**Asymptotic convergence of spectral inverse iterations for stochastic eigenvalue problems.** / Hakula, Harri; Laaksonen, Mikael.

Research output: Contribution to journal › Article

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*Numerische Mathematik*, vol. 142, no. 3, pp. 577-609. https://doi.org/10.1007/s00211-019-01034-w

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*Numerische Mathematik*,

*142*(3), 577-609. https://doi.org/10.1007/s00211-019-01034-w

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TY - JOUR

T1 - Asymptotic convergence of spectral inverse iterations for stochastic eigenvalue problems

AU - Hakula, Harri

AU - Laaksonen, Mikael

PY - 2019/1/1

Y1 - 2019/1/1

N2 - We consider and analyze applying a spectral inverse iteration algorithm and its subspace iteration variant for computing eigenpairs of an elliptic operator with random coefficients. With these iterative algorithms the solution is sought from a finite dimensional space formed as the tensor product of the approximation space for the underlying stochastic function space, and the approximation space for the underlying spatial function space. Sparse polynomial approximation is employed to obtain the first one, while classical finite elements are employed to obtain the latter. An error analysis is presented for the asymptotic convergence of the spectral inverse iteration to the smallest eigenvalue and the associated eigenvector of the problem. A series of detailed numerical experiments supports the conclusions of this analysis.

AB - We consider and analyze applying a spectral inverse iteration algorithm and its subspace iteration variant for computing eigenpairs of an elliptic operator with random coefficients. With these iterative algorithms the solution is sought from a finite dimensional space formed as the tensor product of the approximation space for the underlying stochastic function space, and the approximation space for the underlying spatial function space. Sparse polynomial approximation is employed to obtain the first one, while classical finite elements are employed to obtain the latter. An error analysis is presented for the asymptotic convergence of the spectral inverse iteration to the smallest eigenvalue and the associated eigenvector of the problem. A series of detailed numerical experiments supports the conclusions of this analysis.

UR - http://www.scopus.com/inward/record.url?scp=85063202430&partnerID=8YFLogxK

U2 - 10.1007/s00211-019-01034-w

DO - 10.1007/s00211-019-01034-w

M3 - Article

VL - 142

SP - 577

EP - 609

JO - Numerische Mathematik

JF - Numerische Mathematik

SN - 0029-599X

IS - 3

ER -

ID: 32707433