Freitag, M. and Spence, A., 2007. Convergence theory for inexact inverse iteration applied to the generalised nonsymmetric eigenproblem. Electronic Transactions on Numerical Analysis, 28, pp. 40-67.
In this paper we consider the computation of a finite eigenvalue and corresponding right eigenvector of a large sparse generalised eigenproblem Ax = Mx using inexact inverse iteration. Our convergence theory is quite general and requires few assumptions on A and M. In particular, there is no need for M to be symmetric positive definite or even nonsingular. The theory includes both fixed and variable shift strategies, and the bounds obtained are improvements on those currently in the literature. In addition, the analysis developed here is used to provide a convergence theory for a verson of inexact simplified Jacobi-Davidson. Several numerical examples are presented to illustrate the theory: including applications in nuclear reactor stability, with M singular and nonsymmetric, the linearised Navier-Stokes equations and the bounded finline dielectric waveguide
|Item Type ||Articles|
|Creators||Freitag, M.and Spence, A.|
|Uncontrolled Keywords||nonsymmetric generalised eigenproblem,inexact inverse iteration|
|Departments||Faculty of Science > Mathematical Sciences|
|Publisher Statement||Spence_ETNA_accepted.pdf: This is the author's final, peer-reviewed version of this document, posted with the publisher's permission|
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