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.
- inverse of lower triangular Toeplitz matrix
- Abel equation
- Brunner’s conjecture
Liu, X., McKee, S., Yuan, J. Y., & 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), 1157-1170. https://doi.org/10.1016/j.laa.2011.02.044