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Article: Estimates of the spectral condition number

TitleEstimates of the spectral condition number
Authors
Lam, JLi, ZWei, YFeng, JChung, KW
KeywordsCondition number
Frobenius norm
Singular value
Spectral norm
Issue Date2011
PublisherTaylor & Francis Ltd. The Journal's web site is located at http://www.tandf.co.uk/journals/titles/03081087.asp
Citation
Linear And Multilinear Algebra, 2011, v. 59 n. 3, p. 249-260 How to Cite?
DOI: http://dx.doi.org/10.1080/03081080903369419
AbstractIn this article, new upper and lower bounds for the spectral condition number are obtained. These bounds are constructed based on the Frobenius norm of some matrices related to the given matrix and its inverse. Hence, unlike some existing bounds, these new bounds are smooth functions with respect to the elements in the matrix. It is theoretically established that the new bounds are also sandwiched by the true value of the spectral condition number and its estimates using the Frobenius norms. Moreover, the bounds give the exact value of the spectral condition number when the matrix is unitary or of order less than 3. The new upper bound provided, via statistical numerical comparison, is shown to be the best when compared with existing results. © 2011 Taylor & Francis.
Persistent Identifierhttp://hdl.handle.net/10722/139431
ISSN
0308-1087
2021 Impact Factor: 1.178
2020 SCImago Journal Rankings: 0.688
ISI Accession Number ID
WOS:000287730400003
Funding AgencyGrant Number
RGC HKU7031/06P
National Natural Science Foundation of China10871051
60974137
Shanghai Science and Technology Committee09DZ2272900
Shanghai Municipal Education Committee
973 Program2010CB327900
Independent Innovation Foundation of Shandong University
Ministry of Education20090071110003
Funding Information:

This work was partially supported by RGC HKU 7031/06P, National Natural Science Foundation of China under grant nos 10871051 and 60974137, Shanghai Science and Technology Committee under grant no. 09DZ2272900, Shanghai Municipal Education Committee (Dawn Project), 973 Program Project (no. 2010CB327900), Independent Innovation Foundation of Shandong University and Doctoral Program of the Ministry of Education (no. 20090071110003).

References
References in Scopus

 

DC FieldValueLanguage
dc.contributor.authorLam, Jen_HK
dc.contributor.authorLi, Zen_HK
dc.contributor.authorWei, Yen_HK
dc.contributor.authorFeng, Jen_HK
dc.contributor.authorChung, KWen_HK
dc.date.accessioned2011-09-23T05:49:25Z-
dc.date.available2011-09-23T05:49:25Z-
dc.date.issued2011en_HK
dc.identifier.citationLinear And Multilinear Algebra, 2011, v. 59 n. 3, p. 249-260en_HK
dc.identifier.issn0308-1087en_HK
dc.identifier.urihttp://hdl.handle.net/10722/139431-
dc.description.abstractIn this article, new upper and lower bounds for the spectral condition number are obtained. These bounds are constructed based on the Frobenius norm of some matrices related to the given matrix and its inverse. Hence, unlike some existing bounds, these new bounds are smooth functions with respect to the elements in the matrix. It is theoretically established that the new bounds are also sandwiched by the true value of the spectral condition number and its estimates using the Frobenius norms. Moreover, the bounds give the exact value of the spectral condition number when the matrix is unitary or of order less than 3. The new upper bound provided, via statistical numerical comparison, is shown to be the best when compared with existing results. © 2011 Taylor & Francis.en_HK
dc.languageengen_US
dc.publisherTaylor & Francis Ltd. The Journal's web site is located at http://www.tandf.co.uk/journals/titles/03081087.aspen_HK
dc.relation.ispartofLinear and Multilinear Algebraen_HK
dc.subjectCondition numberen_HK
dc.subjectFrobenius normen_HK
dc.subjectSingular valueen_HK
dc.subjectSpectral normen_HK
dc.titleEstimates of the spectral condition numberen_HK
dc.typeArticleen_HK
dc.identifier.emailLam, J:james.lam@hku.hken_HK
dc.identifier.authorityLam, J=rp00133en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1080/03081080903369419en_HK
dc.identifier.scopuseid_2-s2.0-79951977018en_HK
dc.identifier.hkuros196473en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-79951977018&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume59en_HK
dc.identifier.issue3en_HK
dc.identifier.spage249en_HK
dc.identifier.epage260en_HK
dc.identifier.isiWOS:000287730400003-
dc.publisher.placeUnited Kingdomen_HK
dc.identifier.scopusauthoridLam, J=7201973414en_HK
dc.identifier.scopusauthoridLi, Z=36994622700en_HK
dc.identifier.scopusauthoridWei, Y=35325769700en_HK
dc.identifier.scopusauthoridFeng, J=35744477900en_HK
dc.identifier.scopusauthoridChung, KW=7404086437en_HK
dc.identifier.citeulike8924459-
dc.identifier.issnl0308-1087-

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