In linear stability analysis of a large-scale dynamical system, we need to compute the rightmost eigenvalue(s) for a series of large generalized eigenvalue problems. Existing iterative eigenvalue solvers are not robust when no estimate of the rightmost eigenvalue(s) is available. In this study, we show that such an estimate can be obtained from Lyapunov inverse iteration applied to a special ei...

The FEAST algorithm [5] is an algorithm aimed at solving generalized eigenvalue problems AX = BXΛ, where A,B are n×n matrices. In [4] we presented a short analysis of FEAST involving this eigenvalue problem. In the present work we focus on the real symmetric eigenvalue problem AX = XΛ, where A = A, XX = I and Λ is a diagonal matrix consisting of real eigenvalues. These eigenvalues are sought in...

In earlier papers, the Bauer–Fike technique was applied to the ordinary eigenvalue problem Ax = λx, the generalized eigenvalue problem Ax = λBx and the matrix polynomial eigenvalue problem ∑m k=0 λAkx = 0. General multiple eigenvalues were dealt with and condition numbers were obtained for individual as well as clusters of eigenvalues. In this paper, we shall generalize the technique to the eig...

Stability parameters for stabilized methods in uids are suggested. The computation of the largest eigenvalue of a generalized eigenvalue problem replaces controversial de nitions of element diameters and inverse estimate constants, used heretofore to compute these stability parameters. The design is employed in the advective-di usive model, incompressible Navier-Stokes equations and the Stokes ...

A generalized matrix product can be formally written as A sp p A sp−1 p−1 · · ·A s2 2 A s1 1 , where si ∈ {−1,+1} and (A1, . . . , Ap) is a tuple of (possibly rectangular) matrices of suitable dimensions. The periodic eigenvalue problem related to such a product represents a nontrivial extension of generalized eigenvalue and singular value problems. While the classification of generalized matri...