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Xin Liu (liuxinlsec.cc.ac.cn) Abstract: The uniform bound of 1norm 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 onepoint collocation method for the Abel's equation. In addition, the recent conjecture of Gauthier et al is proved. Keywords: uniform upper bound, 1norm upper bound, infinitynorm 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: Download: [PDF] Entry Submitted: 09/20/2010 Modify/Update this entry  
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