Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/61007
DC FieldValueLanguage
dc.contributorDepartment of Applied Mathematics-
dc.creatorChen, Y-
dc.creatorQi, L-
dc.creatorWang, Q-
dc.date.accessioned2016-12-19T08:54:22Z-
dc.date.available2016-12-19T08:54:22Z-
dc.identifier.issn0377-0427-
dc.identifier.urihttp://hdl.handle.net/10397/61007-
dc.language.isoenen_US
dc.publisherElsevieren_US
dc.subjectGenerating vectoren_US
dc.subjectHankel tensoren_US
dc.subjectPNS-freeen_US
dc.subjectPositive semi-definitenessen_US
dc.subjectSum of squaresen_US
dc.titlePositive semi-definiteness and sum-of-squares property of fourth order four dimensional hankel tensorsen_US
dc.typeJournal/Magazine Articleen_US
dc.identifier.spage356-
dc.identifier.epage368-
dc.identifier.volume302-
dc.identifier.doi10.1016/j.cam.2016.02.019-
dcterms.abstractA symmetric positive semi-definite (PSD) tensor, which is not sum-of-squares (SOS), is called a PSD non-SOS (PNS) tensor. Is there a fourth order four dimensional PNS Hankel tensor? The answer for this question has both theoretical and practical significance. Under the assumptions that the generating vector v of a Hankel tensor A is symmetric and the fifth element v4 of v is fixed at 1, we show that there are two surfaces M0 and N0 with the elements v2,v6,v1,v3,v5 of v as variables, such that M0≥N0, A is SOS if and only if v0≥M0, and A is PSD if and only if v0≥N0, where v0 is the first element of v. If M0=N0 for a point P=(v2,v6,v1,v3,v5)T, there are no fourth order four dimensional PNS Hankel tensors with symmetric generating vectors for such v2,v6,v1,v3,v5. Then, we call such P a PNS-free point. We prove that a 45-degree planar closed convex cone, a segment, a ray and an additional point are PNS-free. Numerical tests check various grid points and report that they are all PNS-free.-
dcterms.bibliographicCitationJournal of computational and applied mathematics, 2016, v. 302, p. 356-368-
dcterms.isPartOfJournal of computational and applied mathematics-
dcterms.issued2016-
dc.identifier.isiWOS:000374601100026-
dc.identifier.scopus2-s2.0-84960107364-
dc.identifier.ros2016002680-
dc.identifier.eissn1879-1778-
dc.identifier.rosgroupid2016002624-
dc.description.ros2016-2017 > Academic research: refereed > Publication in refereed journal-
dc.description.validate201804_a bcma-
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