Condition Numbers of Hessenberg Companion Matrices
Rings and Algebras
2023-02-01 v1
Abstract
The Fiedler matrices are a large class of companion matrices that include the well-known Frobenius companion matrix. The Fiedler matrices are part of a larger class of companion matrices that can be characterized with a Hessenberg form. In this paper, we demonstrate that the Hessenberg form of the Fiedler companion matrices provides a straight-forward way to compare the condition numbers of these matrices. We also show that there are other companion matrices which can provide a much smaller condition number than any Fiedler companion matrix. We finish by exploring the condition number of a class of matrices obtained from perturbing a Frobenius companion matrix while preserving the characteristic polynomial.
Keywords
Cite
@article{arxiv.2301.13257,
title = {Condition Numbers of Hessenberg Companion Matrices},
author = {Michael Cox and Kevin N. Vander Meulen and Adam Van Tuyl and Joseph Voskamp},
journal= {arXiv preprint arXiv:2301.13257},
year = {2023}
}
Comments
16 pages; comments welcomed