Upper bounds for the condition numbers of the GCD and the reciprocal GCD matrices in spectral norm
| dc.contributor.author | Ipek, Ahmet | |
| dc.date.accessioned | 2024-09-18T20:25:18Z | |
| dc.date.available | 2024-09-18T20:25:18Z | |
| dc.date.issued | 2012 | |
| dc.department | Hatay Mustafa Kemal Üniversitesi | en_US |
| dc.description.abstract | Let S = {x(1), . . . , x(n)} be a set of n distinct positive integers. The n x n matrix having the greatest common divisor (x(i), x(j)) of x(i) and x(j) as its i, j-entry is called the greatest common divisor (GCD) matrix defined on S, denoted by ((x(i), x(j))), or abbreviated as (S). The n x n matrix (S-1) = (g(ij)), where g(ij) = 1/(x(i),x(j)) is called the reciprocal greatest common divisor (GCD) matrix on S. In this paper, we present upper bounds for the spectral condition numbers of the reciprocal GCD matrix (S-1) and the GCD matrix (S) defined on S = {1, 2, . . . , n}, with n >= 2, as a function of Euler's phi function and n. (C) 2011 Elsevier Ltd. All rights reserved. | en_US |
| dc.identifier.doi | 10.1016/j.camwa.2011.11.016 | |
| dc.identifier.endpage | 651 | en_US |
| dc.identifier.issn | 0898-1221 | |
| dc.identifier.issue | 3 | en_US |
| dc.identifier.scopus | 2-s2.0-84855818840 | en_US |
| dc.identifier.scopusquality | Q1 | en_US |
| dc.identifier.startpage | 645 | en_US |
| dc.identifier.uri | https://doi.org/10.1016/j.camwa.2011.11.016 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.12483/10228 | |
| dc.identifier.volume | 63 | en_US |
| dc.identifier.wos | WOS:000300756500005 | en_US |
| dc.identifier.wosquality | Q1 | en_US |
| dc.indekslendigikaynak | Web of Science | en_US |
| dc.indekslendigikaynak | Scopus | en_US |
| dc.language.iso | en | en_US |
| dc.publisher | Pergamon-Elsevier Science Ltd | en_US |
| dc.relation.ispartof | Computers & Mathematics With Applications | en_US |
| dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
| dc.rights | info:eu-repo/semantics/openAccess | en_US |
| dc.subject | GCD matrices | en_US |
| dc.subject | Matrix norms | en_US |
| dc.subject | Euler's phi function | en_US |
| dc.title | Upper bounds for the condition numbers of the GCD and the reciprocal GCD matrices in spectral norm | en_US |
| dc.type | Article | en_US |
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