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

Xin Liu (liuxin***at***lsec.cc.ac.cn)
Sean McKee (s.mckee***at***strath.ac.uk)
Jinyun Yuan (yuanjy***at***gmail.com)
Yaxiang Yuan (yyx***at***lsec.cc.ac.cn)

Abstract: The uniform bound of 1-norm is given for the inverse of lower triangular Toeplitz matrices with nonnegative monotonic decreasing entries whose limit is zero. The new bound is the sharpest under the given constraints. This result is then employed to resolve a long standing open problem posed by Brunner concerning the convergence of the one-point collocation method for the Abel's equation. In addition, the recent conjecture of Gauthier et al is proved.

Keywords: uniform upper bound, 1-norm upper bound, infinity-norm upper bound, inverse of lower triangular Toeplitz matrix, Brunner's conjecture, Volterra integral equation, Abel's equation, Abel's matrix.

Category 1: Other Topics (Other )

Citation:

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Entry Submitted: 09/20/2010
Entry Accepted: 09/20/2010
Entry Last Modified: 10/01/2010

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