Article ID Journal Published Year Pages File Type
4602179 Linear Algebra and its Applications 2009 18 Pages PDF
Abstract

We incorporate our recent preconditioning techniques into the classical inverse power (Rayleigh quotient) iteration for computing matrix eigenvectors. Every loop of this iteration essentially amounts to solving an ill conditioned linear system of equations. Due to our modification we solve a well conditioned linear system instead. We prove that this modification preserves local quadratic convergence, show experimentally that fast global convergence is preserved as well, and yield similar results for higher order inverse iteration, covering the cases of multiple and clustered eigenvalues.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory