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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.

Item type: Article
ID code: 30711
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: 24 Jul 2015 09:04
Related URLs:
URI: http://strathprints.strath.ac.uk/id/eprint/30711

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