Asymptotic behavior of the condition number of two-level Toeplitz matrix sequences
type: Item
instance of: scholarly article
title: Asymptotic behavior of the condition number of two-level Toeplitz matrix sequences
zbMATH Open document ID: 1066.15002
published in: Linear Algebra and its Applications
publication date: 2005-02-23T00:00:00Z
review text: The main objective of this paper is the analysis of the Euclidean conditioning \(k\left( \cdot \right) \) of two-level Toeplitz matrices of the form \(T_{nm}\left( f\right) \) where \(n\) and \(m\) are large and the symbol \(f\) is assumed to be \(L^{\infty }\) over \(I^{2}=\left( -\pi ,\pi \right] ^{2}\) and weakly sectorial. It is shown that the upper bound of the condition number will depend on the maximal order of the essential zeros of \(\text{Re}f \); the presence of large \(\text{Im}f\) will decrease the condition number.
Mathematics Subject Classification ID: 15A12
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 2137790
zbMATH Keywords: two-level Toeplitz matrix
zbMATH Keywords: condition number
zbMATH Keywords: essential zeros
zbMATH Keywords: Weakly sectorial symbol
zbMATH Keywords: (Asymptotic) conditioning
author: Dimitrios Noutsos
author: Stefano Serra Capizzano
author: P. Vassalos
reviewed by: Nicholas Karampetakis
MaRDI profile type: Publication
full work available at URL: j.laa.2004.07.014
OpenAlex ID: W2136826453
Wikidata QID: Q112882143
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cites work: Q3254471
DOI: 10.1016/J.LAA.2004.07.014
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description: scientific article; zbMATH DE number 2137790