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Uniform bounds on the 1-norm of the inverse of lower triangular Toeplitz matrices |
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| Authors: | X Liu YX Yuan |
| Institution: | a Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS, CAS, Beijing 100190, China b Department of Mathematics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, UK c Departamento de Matemática - UFPR, Centro Politénico, CP: 19.081, 81531-980 Curitiba, Brazil |
| 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 collocation method for the Abel equation. In addition, the recent conjecture of Gauthier et al. is proved. |
| Keywords: | 15A09 39A10 61A45 65R20 34K28 47B35 74B10 34K06 90C33 15A57 15A0 |
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