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Article: Numerical ranges of tensors

TitleNumerical ranges of tensors
Authors
Ke, RihuanLi, WenNg, Michael K.
KeywordsTensors
Numerical range
Eigenvalues
Convexity
Approximation
Issue Date2016
Citation
Linear Algebra and Its Applications, 2016, v. 508, p. 100-132 How to Cite?
DOI: http://dx.doi.org/10.1016/j.laa.2016.07.003
Abstract© 2016 Elsevier Inc. The main aim of this paper is to generalize matrix numerical ranges to the tensor case based on tensor norms. We show that the basic properties of matrix numerical ranges such as compactness and convexity are valid for tensor numerical ranges. We make use of convexity property to propose an algorithm for approximating tensor numerical ranges in which tensor eigenvalues are contained. Also we consider tensor numerical ranges based on inner products, however, they may not be convex in general.
Persistent Identifierhttp://hdl.handle.net/10722/277036
ISSN
0024-3795
2023 Impact Factor: 1.0
2023 SCImago Journal Rankings: 0.837
ISI Accession Number ID
WOS:000383814400008

 

DC FieldValueLanguage
dc.contributor.authorKe, Rihuan-
dc.contributor.authorLi, Wen-
dc.contributor.authorNg, Michael K.-
dc.date.accessioned2019-09-18T08:35:24Z-
dc.date.available2019-09-18T08:35:24Z-
dc.date.issued2016-
dc.identifier.citationLinear Algebra and Its Applications, 2016, v. 508, p. 100-132-
dc.identifier.issn0024-3795-
dc.identifier.urihttp://hdl.handle.net/10722/277036-
dc.description.abstract© 2016 Elsevier Inc. The main aim of this paper is to generalize matrix numerical ranges to the tensor case based on tensor norms. We show that the basic properties of matrix numerical ranges such as compactness and convexity are valid for tensor numerical ranges. We make use of convexity property to propose an algorithm for approximating tensor numerical ranges in which tensor eigenvalues are contained. Also we consider tensor numerical ranges based on inner products, however, they may not be convex in general.-
dc.languageeng-
dc.relation.ispartofLinear Algebra and Its Applications-
dc.subjectTensors-
dc.subjectNumerical range-
dc.subjectEigenvalues-
dc.subjectConvexity-
dc.subjectApproximation-
dc.titleNumerical ranges of tensors-
dc.typeArticle-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1016/j.laa.2016.07.003-
dc.identifier.scopuseid_2-s2.0-84978401461-
dc.identifier.volume508-
dc.identifier.spage100-
dc.identifier.epage132-
dc.identifier.isiWOS:000383814400008-
dc.identifier.issnl0024-3795-

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