Liu, X. and McKee, S. and Yuan, J.Y. and Yuan, Y.X. (2011) Uniform bounds on the 1norm of the inverse of lower triangular Toeplitz matrices. Linear Algebra and Its Applications, 435 (1). pp. 11571170. ISSN 00243795

PDF
conjecture_proved.pdf  Draft Version Download (690kB)  Preview 
Abstract
A uniform bound on the 1norm is given for the inverse of a lower triangular Toeplitz matrix with nonnegative 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 onepoint collocationmethod for the Abel equation. In addition, the recent conjecture of Gauthier et al. is proved.
Item type:  Article 

ID code:  30711 
Keywords:  inverse of lower triangular Toeplitz matrix , Abel equation, Brunner’s conjecture, Probabilities. Mathematical statistics, Discrete Mathematics and Combinatorics, Algebra and Number Theory, Geometry and Topology, Numerical Analysis 
Subjects:  Science > Mathematics > Probabilities. Mathematical statistics 
Department:  Faculty of Science > Mathematics and Statistics 
Depositing user:  Pure Administrator 
Date Deposited:  27 May 2011 14:38 
Last modified:  18 Jun 2015 17:00 
Related URLs:  
URI:  http://strathprints.strath.ac.uk/id/eprint/30711 
Actions (login required)
View Item 