Using Generalized Cayley Transformations within an Inexact Rational Krylov Sequence Method

Authors:
R. B. Lehoucq;Karl Meerbergen
Affiliations:
-;-
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
1999

Citing 0
Cited 4

Numerical simulation of three dimensional pyramid quantum dot

Journal of Computational Physics
A preconditioned Krylov technique for global hydrodynamic stability analysis of large-scale compressible flows

Journal of Computational Physics
On the Convergence of Rational Ritz Values

SIAM Journal on Matrix Analysis and Applications
Inverse Iteration for Purely Imaginary Eigenvalues with Application to the Detection of Hopf Bifurcations in Large-Scale Problems

SIAM Journal on Matrix Analysis and Applications

Quantified Score

Hi-index	0.01

Visualization

Abstract

The rational Krylov sequence (RKS) method is a generalization of Arnoldi's method. It constructs an orthogonal reduction of a matrix pencil into an upper Hessenberg pencil. The RKS method is useful when the matrix pencil may be efficiently factored. This paper considers approximately solving the resulting linear systems with iterative methods. We show that a Cayley transformation leads to a more efficient and robust eigensolver than the usual shift-invert transformation when the linear systems are solved inexactly within the RKS method. A relationship with the recently introduced Jacobi--Davidson method is also established.