Displaying similar documents to “Algorithms. 42. BISEC. The eigenvalues of the symmetric eigenproblem 𝐀 x = λ 𝐁 x and related eigenproblems”

A modified Cayley transform for the discretized Navier-Stokes equations

K. A. Cliffe, T. J. Garratt, Alastair Spence (1993)

Applications of Mathematics

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This paper is concerned with the problem of computing a small number of eigenvalues of large sparse generalized eigenvalue problems. The matrices arise from mixed finite element discretizations of time dependent equations modelling viscous incompressible flow. The eigenvalues of importance are those with smallest real part and are used to determine the linearized stability of steady states, and could be used in a scheme to detect Hopf bifurcations. We introduce a modified Cayley transform...

Central limit theorems for eigenvalues of deformations of Wigner matrices

M. Capitaine, C. Donati-Martin, D. Féral (2012)

Annales de l'I.H.P. Probabilités et statistiques

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In this paper, we study the fluctuations of the extreme eigenvalues of a spiked finite rank deformation of a Hermitian (resp. symmetric) Wigner matrix when these eigenvalues separate from the bulk. We exhibit quite general situations that will give rise to universality or non-universality of the fluctuations, according to the delocalization or localization of the eigenvectors of the perturbation. Dealing with the particular case of a spike with multiplicity one, we also establish a necessary...