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

Liu, X. and McKee, S. and Yuan, J.Y. and Yuan, Y.X. (2011) Uniform bounds on the 1-norm of the inverse of lower triangular Toeplitz matrices. Linear Algebra and its Applications, 435 (1). pp. 1157-1170. ISSN 0024-3795

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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.

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  Item type:	Article
  ID code:	30711
  Dates:	Date Event 2011 Published 30 March 2011 Published Online
  Keywords:	inverse of lower triangular Toeplitz matrix , Abel equation, Brunner’s conjecture, Probabilities. Mathematical statistics, Discrete Mathematics and Combinatorics, Algebra and Number Theory, Geometry and Topology, Numerical Analysis
  Subjects:	Science > Mathematics > Probabilities. Mathematical statistics
  Department:	Faculty of Science > Mathematics and Statistics
  Depositing user:	Pure Administrator
  Date deposited:	27 May 2011 14:38
  Last modified:	01 Oct 2021 01:39
  Related URLs:	Scopus publication
  URI:	https://strathprints.strath.ac.uk/id/eprint/30711