On the Decay of the Elements of Inverse Triangular Toeplitz Matrices

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 fundame...

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Bibliographic Details
Published in:SIAM journal on matrix analysis and applications 2014-01, Vol.35 (4), p.1288-1302
Main Authors: Ford, Neville J., Savostyanov, Dmitry V., Zamarashkin, Nickolai L.
Format: Article
Language:English
Subjects:
Decay
Decay rate
Inverse
Mathematical models
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Summary: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.
ISSN:0895-4798
1095-7162
DOI:10.1137/130931734