Bounds for Inverses of Triangular Toeplitz Matrices

This short note provides an improvement on a recent result of Vecchio on a norm bound for the inverse of a lower triangular Toeplitz matrix with nonnegative entries. A sharper asymptotic bound is obtained as well as a version for matrices of finite order. The results are shown to be nearly best possible under the given constraints. 1. Introduction. This paper provides an improvement on a recent result of Vecchio on inverses of lower triangular Toeplitz matrices. We refer the reader to Vecchio [13] for discussion of applications particularly those to stability analysis of linear methods for solving Volterra integral equations. Example 1, below, displays an improvement in that realm. The matrices of interest here are (n + 1) × (n + 1) truncations of infinite lower triangular matrices generated by sequences {a i } i≥0 , ie.