Block LU factors of generalized companion matrix pencils

Authors:
A. Amiraslani;D. A. Aruliah;R. M. Corless
Affiliations:
Department of Mathematics and Statistics, University of Calgary, 2500 University Dr. NW, Calgary, AB T2N 1N4, Canada;Faculty of Science, University of Ontario Institute of Technology, Oshawa, ON L1H 7K4, Canada;Department of Applied Mathematics, University of Western Ontario, London, ON N6A 5B7, Canada
Venue:
Theoretical Computer Science
Year:
2007

Citing 11
Cited 1

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Abstract

We present formulas for computations involving companion matrix pencils as may arise in considering polynomial eigenvalue problems. In particular, we provide explicit companion matrix pencils for matrix polynomials expressed in a variety of polynomial bases including monomial, orthogonal, Newton, Lagrange, and Bernstein/Bezier bases. Additionally, we give a pair of explicit LU factors associated with each pencil and a prescription for block pivoting when required.