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.

    Creators(s): Liu, X., McKee, S., Yuan, J.Y. and Yuan, Y.X.;
    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:02 Feb 2021 01:55
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/30711
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