Contributions to Books:
"Normal forms for companion matrices and contractivity in inner product norms";
in: "ASC Report No. 24/2009",
issued by: Institute for Analysis and Scientific Computing;
Vienna University of Technology,
We study the problem of finding a inner product norm in which a given companion matrix with a [weakly] stable spectrum becomes contractive (or dissipative), via a preferably well-conditioned change of basis. To this end we use a basis transformation related to a rescaled LQ decomposition of the associated Vandermonde matrix which is robust to w.r.t. confluent or non-confluent spectra. For n=2 we give an explicit construction. The transformed, contractive matrix is non-normal in general, and it depends on the distribution of the spectrum in a nonlinear way. This analysis cannot be directly generalized to higher dimension, but it suggests an algebraic/numerical algorithm for a numerically given spectrum. This has been tested for small values of n and appears to be successful.
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.