On the estimation of the q-numerical range of monic matrix polynomials

Psarrakos, PJ

dc.contributor.author	Psarrakos, PJ	en
dc.date.accessioned	2014-03-01T01:21:10Z
dc.date.available	2014-03-01T01:21:10Z
dc.date.issued	2004	en
dc.identifier.issn	1068-9613	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16110
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-3042623839&partnerID=40&md5=85f3139d6644a983b8332710b08844db	en
dc.subject	Boundary	en
dc.subject	Davis-Wielandt shell	en
dc.subject	Eigenvalue	en
dc.subject	Inner q-numerical radius	en
dc.subject	Matrix polynomial	en
dc.subject	q-numerical range	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	BOUNDARY	en
dc.title	On the estimation of the q-numerical range of monic matrix polynomials	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	2004	en
heal.abstract	For a given q is an element of [0, 1], the q-numerical range of an n x n matrix polynomial P(lambda) = I lambda(m) + A(m-1)lambda(m-1) +...+ A(1)lambda + A(0) is defined by W-q(P) = {lambda is an element of C: yP(lambda)x = 0, x y is an element of C-n, xx = yy = 1, y x = q}. In this paper, an inclusion-exclusion methodology for the estimation of W-q(P) is proposed. Our approach is based on i) the discretization of a region Omega that contains W-q(P), and ii) the construction of an open circular disk, which does not intersect W-q(P), centered at every grid point mu is an element of Omega\W-q(P). For the cases q = 1 and 0 < q < 1, an important difference arises in one of the steps of the algorithm. Thus, these two cases are discussed separately.	en
heal.publisher	KENT STATE UNIVERSITY	en
heal.journalName	Electronic Transactions on Numerical Analysis	en
dc.identifier.isi	ISI:000228145300001	en
dc.identifier.volume	17	en
dc.identifier.spage	1	en
dc.identifier.epage	10	en