Spectral bounds for \(\| A^{-1}\| _{\infty}\)
type: Item
instance of: scholarly article
title: Spectral bounds for \(\| A^{-1}\| _{\infty}\)
zbMATH Open document ID: 0618.41012
DOI: 10.1016/0021-9045(86)90005-5
author: Stephen Demko
published in: Journal of Approximation Theory
publication date: 1986-01-01T00:00:00Z
review text: The author studies the spectral bounds for \(\| A^{- 1}\|_{\infty}\), where A is a positive definite Hermitian matrix. In the main theorem of the paper it is proved that if \(A^ m\) has no more than km non-zero entries in each row then we obtain \(\| A^{- 1}\|_{\infty}\leq 33\sqrt{k}\| A\|_ 2^{1/4}\| A^{- 1}\|_ 2^{5/4}.\) The author conjectures that the index 5/4 could be lowered to 1, perhaps with associated changes in the remaining quantities. In another proposition it is shown that if A belongs to a certain subclass of bi-infinite Hermitian Toeplitz matrices then \(\| A^{-1}\|_ 2=\| A^{-1}\|_{\infty}\).
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A50
Mathematics Subject Classification ID: 41A58
zbMATH DE Number: 4002725
zbMATH Keywords: spectral bounds
zbMATH Keywords: positive definite Hermitian matrix
zbMATH Keywords: bi-infinite Hermitian Toeplitz matrices
reviewed by: Ganesh Datta Dikshit
MaRDI profile type: Publication
full work available at URL: 0021-9045(86)90005-5
OpenAlex ID: W2050036528
cites work: Inverses of Band Matrices and Local Convergence of Spline Projections
cites work: Decay Rates for Inverses of Band Matrices
cites work: Q3671491
cites work: \(L_\infty\)-boundedness of \(L_ 2-\)projections on splines for a geometric mesh
description: scientific article; zbMATH DE number 4002725