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

X. Liu, S. McKee, J.Y. Yuan, Y.X. Yuan

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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.
Original languageEnglish
Pages (from-to)1157-1170
Number of pages14
JournalLinear Algebra and its Applications
Volume435
Issue number1
Early online date30 Mar 2011
DOIs
Publication statusPublished - 2011

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Keywords

  • inverse of lower triangular Toeplitz matrix
  • Abel equation
  • Brunner’s conjecture

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