In:
Numerical Linear Algebra with Applications, Wiley, Vol. 23, No. 2 ( 2016-03), p. 314-339
Abstract:
We describe randomized algorithms for computing the dominant eigenmodes of the generalized Hermitian eigenvalue problem A x = λ B x , with A Hermitian and B Hermitian and positive definite. The algorithms we describe only require forming operations A x , B x and B −1 x and avoid forming square roots of B (or operations of the form, B 1/2 x or B −1/2 x ). We provide a convergence analysis and a posteriori error bounds and derive some new results that provide insight into the accuracy of the eigenvalue calculations. The error analysis shows that the randomized algorithm is most accurate when the generalized singular values of B −1 A decay rapidly. A randomized algorithm for the generalized singular value decomposition is also provided. Finally, we demonstrate the performance of our algorithm on computing an approximation to the Karhunen–Loève expansion, which involves a computationally intensive generalized Hermitian eigenvalue problem with rapidly decaying eigenvalues. Copyright © 2015 John Wiley & Sons, Ltd.
Type of Medium:
Online Resource
ISSN:
1070-5325
,
1099-1506
Language:
English
Publisher:
Wiley
Publication Date:
2016
detail.hit.zdb_id:
2012602-5
SSG:
17,1
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