Uniform bounds on the 1-norm of the inverse of lower triangular Toeplitz matrices

X. Liu, S. McKee, J.Y. Yuan, Y.X. Yuan

Research output: Contribution to journalArticle

2 Citations (Scopus)
88 Downloads (Pure)

Abstract

A uniform bound on the 1-norm is given for the inverse of a lower triangular Toeplitz matrix with non-negative monotonically decreasing entries whose limit is zero. The new bound is sharp under certain specified constraints. This result is then employed to throw light upon a long standing open problem posed by Brunner concerning the convergence of the one-point collocationmethod for the Abel equation. In addition, the recent conjecture of Gauthier et al. is proved.
Original languageEnglish
Pages (from-to)1157-1170
Number of pages14
JournalLinear Algebra and its Applications
Volume435
Issue number1
Early online date30 Mar 2011
DOIs
Publication statusPublished - 2011

Fingerprint

Abel Equation
Uniform Bound
Triangular matrix
Toeplitz matrix
Open Problems
Non-negative
Norm
Zero

Keywords

  • inverse of lower triangular Toeplitz matrix
  • Abel equation
  • Brunner’s conjecture

Cite this

@article{40b13a22a12543ccbc09cf7042e0b399,
title = "Uniform bounds on the 1-norm of the inverse of lower triangular Toeplitz matrices",
abstract = "A uniform bound on the 1-norm is given for the inverse of a lower triangular Toeplitz matrix with non-negative monotonically decreasing entries whose limit is zero. The new bound is sharp under certain specified constraints. This result is then employed to throw light upon a long standing open problem posed by Brunner concerning the convergence of the one-point collocationmethod for the Abel equation. In addition, the recent conjecture of Gauthier et al. is proved.",
keywords = "inverse of lower triangular Toeplitz matrix , Abel equation, Brunner’s conjecture",
author = "X. Liu and S. McKee and J.Y. Yuan and Y.X. Yuan",
year = "2011",
doi = "10.1016/j.laa.2011.02.044",
language = "English",
volume = "435",
pages = "1157--1170",
journal = "Linear Algebra and its Applications",
issn = "0024-3795",
number = "1",

}

Uniform bounds on the 1-norm of the inverse of lower triangular Toeplitz matrices. / Liu, X.; McKee, S.; Yuan, J.Y.; Yuan, Y.X.

In: Linear Algebra and its Applications, Vol. 435, No. 1, 2011, p. 1157-1170.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Uniform bounds on the 1-norm of the inverse of lower triangular Toeplitz matrices

AU - Liu, X.

AU - McKee, S.

AU - Yuan, J.Y.

AU - Yuan, Y.X.

PY - 2011

Y1 - 2011

N2 - A uniform bound on the 1-norm is given for the inverse of a lower triangular Toeplitz matrix with non-negative monotonically decreasing entries whose limit is zero. The new bound is sharp under certain specified constraints. This result is then employed to throw light upon a long standing open problem posed by Brunner concerning the convergence of the one-point collocationmethod for the Abel equation. In addition, the recent conjecture of Gauthier et al. is proved.

AB - A uniform bound on the 1-norm is given for the inverse of a lower triangular Toeplitz matrix with non-negative monotonically decreasing entries whose limit is zero. The new bound is sharp under certain specified constraints. This result is then employed to throw light upon a long standing open problem posed by Brunner concerning the convergence of the one-point collocationmethod for the Abel equation. In addition, the recent conjecture of Gauthier et al. is proved.

KW - inverse of lower triangular Toeplitz matrix

KW - Abel equation

KW - Brunner’s conjecture

UR - http://www.scopus.com/inward/record.url?scp=79958825418&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2011.02.044

DO - 10.1016/j.laa.2011.02.044

M3 - Article

VL - 435

SP - 1157

EP - 1170

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

SN - 0024-3795

IS - 1

ER -