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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Official URL: https://doi.org/10.1016/j.laa.2011.02.044
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.
Creators(s): | Liu, X., McKee, S., Yuan, J.Y. and Yuan, Y.X.; | Item type: | Article |
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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: | 02 Feb 2021 01:55 |
Related URLs: | |
URI: | https://strathprints.strath.ac.uk/id/eprint/30711 |
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