Convergence of inexact inverse iteration with application to preconditioned iterative solvers (Q878195)

This paper is about an inexact inverse iteration applied to the generalized nonsymmetric eigenvalue problem with large and sparse coefficient matrices. It is shown that inexact inverse iteration is a modified Newton method and hence convergence rates for various types of inexact inverse iteration for computing an algebraically simple eigenvalue are obtained. A novel approach to the analysis for variable shifts is used which provides a much simpler analysis, and also suggests a way of analysing preconditioned iterative solvers when the right-hand side is modified.