Year: 2011
Type: preprint
Abstract: The condition numbers $CN(T)==||T|| .||T^{-1}|| $ of Toeplitz and analytic $n\times n$ matrices $T$ are studied. It is shown that the supremum of $CN(T)$ over all such matrices with $||T|| \leq1$ and the given minimum of eigenvalues $r=min_{i=1..n}|λ_{i}|>0$ behaves as the corresponding supremum over all $n\times n$ matrices (i.e., as $\frac{1}{r{}^{n}}$ (Kronecker)), and this equivalence is uniform in $n$ and $r$. The proof is based on a use of the Sarason-Sz.Nagy-Foias commutant lifting theorem.
Source: arXiv (Cornell University)
Author: Zarouf, Rachid
Institution: Institut de Mathématiques de Marseille
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2950974104