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: http://dx.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.

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 |

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Depositing user: | Pure Administrator |

Date Deposited: | 27 May 2011 15:38 |

Last modified: | 27 Mar 2014 22:19 |

URI: | http://strathprints.strath.ac.uk/id/eprint/30711 |

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