Jordan Canonical Form and Power Method

Abstract

It is well-known that computing the eigenvalues and eigenvectors of a given matrix A is difficult in case A is not diagonalizable. In this paper, we apply Power methods with Hotelling's, Frazer-Duncan-Collar's and Wielandt's deflations to such matrices and show the numerical properties. Finally, the error analysis is given, particularly for Power method with Hotelling's deflation, when the Jordan canonical form of A has one 2-dimensional Jordan block.