Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/9151
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dc.contributor.authorChen, Zen_US
dc.contributor.authorQi, Len_US
dc.contributor.authorYang, Qen_US
dc.contributor.authorYang, Yen_US
dc.date.accessioned2014-12-19T06:53:57Z-
dc.date.available2014-12-19T06:53:57Z-
dc.date.issued2013-
dc.identifier.citationLinear algebra and its applications, 2013, v. 439, no. 12, p. 3713-3733en_US
dc.identifier.issn0024-3795-
dc.identifier.urihttp://hdl.handle.net/10397/9151-
dc.description.abstractIn this paper we study two solution methods for finding the largest eigenvalue (singular value) of general square (rectangular) nonnegative tensors. For a positive tensor, one can find the largest eigenvalue (singular value) based on the properties of the positive tensor and the power-type method. While for a general nonnegative tensor, we use a series of decreasing positive perturbations of the original tensor and repeatedly recall power-type method for finding the largest eigenvalue (singular value) of a positive tensor with an inexact strategy. We prove the convergence of the method for the general nonnegative tensor. Under a certain assumption, the computing complexity of the method is established. Motivated by the interior-point method for the convex optimization, we put forward a one-step inner iteration power-type method, whose convergence is also established under certain assumption. Additionally, by using embedding technique, we show the relationship between the singular values of the rectangular tensor and the eigenvalues of related square tensor, which suggests another way for finding the largest singular value of nonnegative rectangular tensor besides direct power-type method for this problem. Finally, numerical examples of our algorithms are reported, which demonstrate the convergence behaviors of our methods and show that the algorithms presented are promising.en_US
dc.description.sponsorshipDepartment of Applied Mathematicsen_US
dc.language.isoenen_US
dc.publisherElsevieren_US
dc.relation.ispartofLinear algebra and its applicationsen_US
dc.subjectAlgorithmen_US
dc.subjectComplexityen_US
dc.subjectConvergenceen_US
dc.subjectEigenvalueen_US
dc.subjectNonnegative tensoren_US
dc.subjectPerturbationen_US
dc.subjectSingular valueen_US
dc.titleThe solution methods for the largest eigenvalue (singular value) of nonnegative tensors and convergence analysisen_US
dc.typeJournal/Magazine Articleen_US
dc.identifier.spage3713-
dc.identifier.epage3733-
dc.identifier.volume439-
dc.identifier.issue12-
dc.identifier.doi10.1016/j.laa.2013.09.027-
dc.identifier.scopus2-s2.0-84889084699-
dc.identifier.eissn1873-1856-
dc.identifier.rosgroupidr68259-
dc.description.ros2013-2014 > Academic research: refereed > Publication in refereed journal-
Appears in Collections:Journal/Magazine Article
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