Two counterexamples related to the Kreiss matrix theorem
type: Item
instance of: scholarly article
title: Two counterexamples related to the Kreiss matrix theorem
zbMATH Open document ID: 0842.15013
DOI: 10.1007/BF01935020
author: J. F. B. M. Kraaijevanger
published in: BIT
publication date: 1996-08-11T00:00:00Z
review text: Let \(A\) be an \(s\times s\) matrix satisfying certain resolvent condition with respect to the unit disk with constant \(K\). A recent version of the Kreiss matrix theorem states that \(|A^n |\leq esK\), \(n\geq 0\). In this paper the author shows that for any fix \(K\geq \pi+1\) the upper bound \(esK\) is sharp in the sense that a linear dependence on the dimension \(s\) is the best possible result. Also, a similar result is obtained for the continuous version, which states that \(|e^{tA} |\leq esK\), \(t>0\), if \(A\) satisfies a resolvent condition with respect to the left half plane with constant \(K\).
Mathematics Subject Classification ID: 15A45
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 716130
zbMATH Keywords: resolvent growth condition
zbMATH Keywords: Kreiss matrix theorem
reviewed by: Ali-Akbar Jafarian
MaRDI profile type: Publication
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Wikidata QID: Q124807420
full work available at URL: https://doi.org/10.1007/bf01935020
OpenAlex ID: W2042032163
description: scientific article; zbMATH DE number 716130