W. Auzinger:

"A note on similarity to contraction for stable 2x2 companion matrices";

in: "ASC Report 01/2013", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2013, ISBN: 978-3-902627-06-3, 1 - 9.

We consider companion matrices of dimension 2 with general complex spectra satisfying a root condition with respect to the closed complex unit circle or the closed left complex half plane. For both cases, smooth and naturally conditioned basis transformations are constructed such that the resulting, transformed matrix is contractive or dissipative, respectively.

companion matrix; stable spectrum; root condition; basis transformation; con- tractivity; dissipativity; distance from instability.

http://www.asc.tuwien.ac.at/preprint/2013/asc01x2013.pdf

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