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 (https://doi.org/10.1016/j.laa.2011.02.044)

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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.

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