Bulgak, AyşeDemidenko, GennadiiMatveeva, Inessa2016-12-092016-12-092003Bulgak, A., Demidenko, G. A., Matveeva, I. (2003). On location of the matrix spectrum inside an elipse. Selcuk Journal of Applied Mathematics, 4 (1), 25-41.1302-7980https://hdl.handle.net/20.500.12395/3465The research was financially supported by the Scientific and Technical Research Council of Turkey (TUBITAK) in the framework of the NATO-PC Fellowships Programme.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 ${cal E}$.eninfo:eu-repo/semantics/openAccessEllipseElipsMatris spektrumuMatris denklemleriMatrix equationsMatrix spectrumMatrix seriesMatris serileriAlgoritmalarAlgorithmsArticle42541