Publisher DOI: 10.1007/s00020-019-2537-z
Title: Lower Bounds for the Smallest Singular Value of Certain Toeplitz-like Triangular Matrices with Linearly Increasing Diagonal Entries
Language: English
Authors: Bünger, Florian 
Rump, Siegfried M. 
Keywords: Frobenius norm;Infinite-dimensional matrix;Minimum singular value;Toeplitz-like triangular matrices
Issue Date: Oct-2019
Source: Integral Equations and Operator Theory 5 (91) : 39 (2019-10)
Journal or Series Name: Integral equations and operator theory 
Abstract (english): Let L be a lower triangular n× n-Toeplitz matrix with first column (μ, α, β, α, β, … ) T, where μ, α, β≥ 0 fulfill α- β∈ [ 0 , 1 ) and α∈ [ 1 , μ+ 3 ]. Furthermore let D be the diagonal matrix with diagonal entries 1 , 2 , … , n. We prove that the smallest singular value of the matrix A: = L+ D is bounded from below by a constant ω= ω(μ, α, β) > 0 which is independent of the dimension n.
ISSN: 0378-620X
Institute: Zuverlässiges Rechnen E-19 
Type: (wissenschaftlicher) Artikel
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