| Home > Publications > Reports > Numerical Analysis and Applied Mathematics (TW) |
TW 538
Steven Delvaux, Katrijn Frederix, Marc Van Barel
An algorithm for computing the eigenvalues of block companion matrices
Abstract
In this paper we propose a method for computing the roots of a monic matrix polynomial. To this end we compute the eigenvalues of the corresponding block companion matrix C. This is done by implementing the QR algorithm in such a way that it exploits the rank structure of the matrix. Because of this structure, we can represent the matrix in Givens-weight representation. A similar method as in [S. Chandrasekaran, M. Gu, J. Xia, and J. Zhu, A fast QR algorithm for companion matrices, Operator Theory: Advances and Applications, 179:111-143, 2007] the bulge chasing, is used during the QR iteration. For practical usage, matrix C has to be brought in Hessenberg form before the QR iteration starts. During the QR iteration and the transformation to Hessenberg form, the property of the matrix being unitary plus low rank numerically deteriorates. A method to restore this property is used.
report.pdf (480K) / mailto: M. Van Barel