On the Decay of the Elements of Inverse Triangular Toeplitz Matrices
Neville J. Ford, Dmitry Savostyanov, Nickolai L. Zamarashkin · SIAM Journal on Matrix Analysis and Applications · 2014
We consider half-infinite triangular Toeplitz matrices with slow decay of the elements and prove under a monotonicity condition that the elements of the inverse matrix, as well as the elements of the fundamental matrix, decay to zero. We provide a quantitative description of the decay of the fundamental matrix in terms of $p$-norms. The results add to the classical results of Jaffard and Vecchio and are illustrated by numerical examples.