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On the decay of the elements of inverse triangular Toeplitz matrices

Ford, Neville J.
; 
Savostyanov, Dmitry V.
; 
Zamarashkin, Nickolai L.
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Affiliation
University of Chester ; University of Chester ; Institute of Numerical Mathematics, Russian Academy of Sciences
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Publication Date
2014-10-28
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Mathematics
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Abstract
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.
Citation
Ford, N. J., Savostyanov, D. V., & Zamarashkin, N. L. (2014). On the decay of the elements of inverse triangular Toeplitz matrices. SIAM Journal on Matrix Analysis and Applications, 35(4), pp. 1288-1302
Publisher
Society for Industrial and Applied Mathematics
Journal
SIMAX (SIAM Journal of Matrix Analysis and Applications)
Research Unit
URI
http://hdl.handle.net/10034/323408
DOI
10.1137/130931734
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PubMed Central ID
Type
Article
Language
en
Description
Series/Report no.
ISSN
0895-4798
EISSN
1095-7162
ISBN
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Sponsors
Leverhulme Trust
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http://www.siam.org/journals/simax.php