On the decay of the elements of inverse triangular Toeplitz matrices

Hdl Handle:
http://hdl.handle.net/10034/323408
Title:
On the decay of the elements of inverse triangular Toeplitz matrices
Authors:
Ford, Neville J.; Savostyanov, Dmitry V.; Zamarashkin, Nickolai L.
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.
Affiliation:
University of Chester ; University of Chester ; Institute of Numerical Mathematics, Russian Academy of Sciences
Citation:
SIAM Journal on Matrix Analysis and Applications, 2014, 35(4), pp. 1288-1302
Publisher:
Society for Industrial and Applied Mathematics
Journal:
SIMAX (SIAM Journal of Matrix Analysis and Applications)
Publication Date:
18-Jul-2014
URI:
http://hdl.handle.net/10034/323408
DOI:
10.1137/130931734
Additional Links:
http://www.siam.org/journals/simax.php
Type:
Article
Language:
en
ISSN:
0895-4798
EISSN:
1095-7162
Sponsors:
Leverhulme Trust
Appears in Collections:
Mathematics

Full metadata record

DC FieldValue Language
dc.contributor.authorFord, Neville J.en
dc.contributor.authorSavostyanov, Dmitry V.en
dc.contributor.authorZamarashkin, Nickolai L.en
dc.date.accessioned2014-07-18T13:08:54Zen
dc.date.available2014-07-18T13:08:54Zen
dc.date.issued2014-07-18en
dc.identifier.citationSIAM Journal on Matrix Analysis and Applications, 2014, 35(4), pp. 1288-1302en
dc.identifier.issn0895-4798en
dc.identifier.doi10.1137/130931734en
dc.identifier.urihttp://hdl.handle.net/10034/323408en
dc.description.abstractWe 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.en
dc.description.sponsorshipLeverhulme Trusten
dc.language.isoenen
dc.publisherSociety for Industrial and Applied Mathematicsen
dc.relation.urlhttp://www.siam.org/journals/simax.phpen
dc.subjectVolterra equationen
dc.subjectAbel equationen
dc.subjectToeplitz matrixen
dc.subjectstability analysisen
dc.titleOn the decay of the elements of inverse triangular Toeplitz matricesen
dc.typeArticleen
dc.identifier.eissn1095-7162en
dc.contributor.departmentUniversity of Chester ; University of Chester ; Institute of Numerical Mathematics, Russian Academy of Sciencesen
dc.identifier.journalSIMAX (SIAM Journal of Matrix Analysis and Applications)en
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