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- Publisher Website: 10.1016/j.laa.2016.07.003
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Article: Numerical ranges of tensors
Title | Numerical ranges of tensors |
---|---|
Authors | |
Keywords | Tensors Numerical range Eigenvalues Convexity Approximation |
Issue Date | 2016 |
Citation | Linear Algebra and Its Applications, 2016, v. 508, p. 100-132 How to Cite? |
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 Identifier | http://hdl.handle.net/10722/277036 |
ISSN | 2023 Impact Factor: 1.0 2023 SCImago Journal Rankings: 0.837 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Ke, Rihuan | - |
dc.contributor.author | Li, Wen | - |
dc.contributor.author | Ng, Michael K. | - |
dc.date.accessioned | 2019-09-18T08:35:24Z | - |
dc.date.available | 2019-09-18T08:35:24Z | - |
dc.date.issued | 2016 | - |
dc.identifier.citation | Linear Algebra and Its Applications, 2016, v. 508, p. 100-132 | - |
dc.identifier.issn | 0024-3795 | - |
dc.identifier.uri | http://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.language | eng | - |
dc.relation.ispartof | Linear Algebra and Its Applications | - |
dc.subject | Tensors | - |
dc.subject | Numerical range | - |
dc.subject | Eigenvalues | - |
dc.subject | Convexity | - |
dc.subject | Approximation | - |
dc.title | Numerical ranges of tensors | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1016/j.laa.2016.07.003 | - |
dc.identifier.scopus | eid_2-s2.0-84978401461 | - |
dc.identifier.volume | 508 | - |
dc.identifier.spage | 100 | - |
dc.identifier.epage | 132 | - |
dc.identifier.isi | WOS:000383814400008 | - |
dc.identifier.issnl | 0024-3795 | - |