dc.contributor.author |
Ozturk, Hasen Mekki |
|
dc.date.accessioned |
2024-03-15T11:13:55Z |
|
dc.date.available |
2024-03-15T11:13:55Z |
|
dc.date.issued |
2023 |
|
dc.identifier.citation |
Öztürk, HM. (2023). On a conjecture of Davies and Levitin. Math. Meth. Appl. Sci., 46(4), 4391-4412. https://doi.org/10.1002/mma.8766 |
en_US |
dc.identifier.issn |
0170-4214 |
|
dc.identifier.issn |
1099-1476 |
|
dc.identifier.uri |
http://dx.doi.org/10.1002/mma.8766 |
|
dc.identifier.uri |
https://www.webofscience.com/wos/woscc/full-record/WOS:000871215300001 |
|
dc.identifier.uri |
http://earsiv.odu.edu.tr:8080/xmlui/handle/11489/4440 |
|
dc.description |
WoS Categories: Mathematics, Applied |
en_US |
dc.description |
Web of Science Index: Science Citation Index Expanded (SCI-EXPANDED) |
en_US |
dc.description |
Research Areas: Mathematics |
en_US |
dc.description.abstract |
Let Hc$$ {H}_c $$ be a (2n)x(2n)$$ (2n)\times (2n) $$ symmetric tridiagonal matrix with diagonal elements c is an element of Double-struck capital R$$ c\in \mathbb{R} $$ and off-diagonal elements one, and S$$ S $$ be a (2n)x(2n)$$ (2n)\times (2n) $$ diagonal matrix with the first n$$ n $$ diagonal elements being plus ones and the last n$$ n $$ being minus ones. Davies and Levitin studied the eigenvalues of a linear pencil Ac=Hc-lambda S$$ {\mathcal{A}}_c={H}_c-\lambda S $$ as 2n$$ 2n $$ approaches to infinity. It was conjectured by DL that for any n is an element of N$$ n\in \mathbb{N} $$ the non-real eigenvalues lambda$$ \lambda $$ of Ac$$ {\mathcal{A}}_c $$ satisfy both |lambda+c|<2$$ \mid \lambda +c\mid and |lambda-c|<2$$ \mid \lambda -c\mid . The conjecture has been verified numerically for a wide range of n$$ n $$ and c$$ c $$, but so far the full proof is missing. The purpose of the paper is to support this conjecture with a partial proof and several numerical experiments which allow to get some insight in the behaviour of the non-real eigenvalues of Ac$$ {\mathcal{A}}_c $$. We provide a proof of the conjecture for n <= 3$$ n\le 3 $$, and also in the case where |lambda+c|=|lambda-c|$$ \mid \lambda +c\mid =\mid \lambda -c\mid $$. In addition, numerics indicate that some phenomena may occur for more general linear pencils. |
en_US |
dc.description.sponsorship |
Ministry of National Education of the Republic of Turkiye |
en_US |
dc.language.iso |
eng |
en_US |
dc.publisher |
WILEY-HOBOKEN |
en_US |
dc.relation.isversionof |
10.1002/mma.8766 |
en_US |
dc.rights |
info:eu-repo/semantics/openAccess |
en_US |
dc.subject |
chebyshev polinomials of the second kind, eigenvalues, linear operator pencils, non-self-adjoint matrices, spectral theory |
en_US |
dc.title |
On a conjecture of Davies and Levitin |
en_US |
dc.type |
article |
en_US |
dc.relation.journal |
MATHEMATICAL METHODS IN THE APPLIED SCIENCES |
en_US |
dc.contributor.department |
Ordu Üniversitesi |
en_US |
dc.contributor.authorID |
0000-0002-4524-651X |
en_US |
dc.identifier.volume |
46 |
en_US |
dc.identifier.issue |
4 |
en_US |
dc.identifier.startpage |
4391 |
en_US |
dc.identifier.endpage |
4412 |
en_US |