On location of the matrix spectrum inside an elipse
| dc.contributor.author | Bulgak, Ayşe | |
| dc.contributor.author | Demidenko, Gennadii | |
| dc.contributor.author | Matveeva, Inessa | |
| dc.date.accessioned | 2016-12-09T08:56:10Z | |
| dc.date.available | 2016-12-09T08:56:10Z | |
| dc.date.issued | 2003 | |
| dc.description | The research was financially supported by the Scientific and Technical Research Council of Turkey (TUBITAK) in the framework of the NATO-PC Fellowships Programme. | en_US |
| dc.description.abstract | In the present article we consider the problem on location of the spectrum of an arbitrary matrix $A$ inside the ellipse calE=lambdainC:frac(Relambda)2a2+frac(Imlambda)2b2=1,quada>b. calE=lambdainC:frac(Relambda)2a2+frac(Imlambda)2b2=1,quada>b. One of the authors (see~[9]) established a connection of the problem with solvability of the matrix equation H?left(frac12a2+frac12b2ight)A?HA?left(frac14a2?frac14b2ight)(HA2+(A?)2H)=C. H?left(frac12a2+frac12b2ight)A?HA?left(frac14a2?frac14b2ight)(HA2+(A?)2H)=C. In this article we construct a Hermitian positive definite solution $H$ to the equation in the form of a power series. We prove that the norm $|H|$ characterizes an immersion depth of eigenvalues of the matrix $A$ in the inside of the ellipse ${cal E}$. On the base of these results we propose an algorithm to determine whether the spectrum of the matrix $A$ belongs to the inside of the ellipse ${cal E}$. | en_US |
| dc.identifier.citation | Bulgak, A., Demidenko, G. A., Matveeva, I. (2003). On location of the matrix spectrum inside an elipse. Selcuk Journal of Applied Mathematics, 4 (1), 25-41. | en_US |
| dc.identifier.endpage | 41 | |
| dc.identifier.issn | 1302-7980 | en_US |
| dc.identifier.startpage | 25 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.12395/3465 | |
| dc.identifier.volume | 4 | |
| dc.language.iso | en | en_US |
| dc.publisher | Selcuk University Research Center of Applied Mathematics | en_US |
| dc.relation.ispartof | Selcuk Journal of Applied Mathematics | en_US |
| dc.relation.publicationcategory | Makale - Kategori Belirlenecek | en_US |
| dc.rights | info:eu-repo/semantics/openAccess | en_US |
| dc.selcuk | 20240510_oaig | en_US |
| dc.subject | Ellipse | en_US |
| dc.subject | Elips | en_US |
| dc.subject | Matris spektrumu | en_US |
| dc.subject | Matris denklemleri | en_US |
| dc.subject | Matrix equations | en_US |
| dc.subject | Matrix spectrum | en_US |
| dc.subject | Matrix series | en_US |
| dc.subject | Matris serileri | en_US |
| dc.subject | Algoritmalar | en_US |
| dc.subject | Algorithms | en_US |
| dc.title | On location of the matrix spectrum inside an elipse | en_US |
| dc.type | Article | en_US |
