On the decay of elements of inverse triangular Toeplitz matrix
Numerical Analysis
2014-10-31 v1 Classical Analysis and ODEs
Abstract
We consider half-infinite triangular Toeplitz matrices with slow decay of the elements and prove under a monotonicity condition that elements of the inverse matrix, as well as elements of the fundamental matrix, decay to zero. We also provide a quantitative description of the decay of the fundamental matrix in terms of p-norms. Finally, we prove that for matrices with slow log-convex decay the inverse matrix has fast decay, i.e. is bounded. The results are compared with the classical results of Jaffard and Veccio and illustrated by numerical example.
Keywords
Cite
@article{arxiv.1308.0724,
title = {On the decay of elements of inverse triangular Toeplitz matrix},
author = {Neville Ford and D. V. Savostyanov and N. L. Zamarashkin},
journal= {arXiv preprint arXiv:1308.0724},
year = {2014}
}