Improved tests and characterizations of totally nonnegative matrices

Publikationstyp: Zeitschriftenartikel
URI (zitierfähiger Link): http://nbn-resolving.de/urn:nbn:de:bsz:352-0-271648
Autor/innen: Adm, Mohammad; Garloff, Jürgen
Erscheinungsjahr: 2014
Erschienen in: Electronic Journal of Linear Algebra (ELA) ; 27 (2014). - S. 588-610. - ISSN 1081-3810. - eISSN 1537-9582
URL der Originalveröffentlichung: http://repository.uwyo.edu/ela/vol27/iss1/255/, Letzter Zugriff am 24. Feb 2015
DOI (zitierfähiger Link): https://dx.doi.org/10.13001/1081-3810.1920
Zusammenfassung:
Totally nonnegative matrices, i.e., matrices having all minors nonnegative, are considered. A condensed form of the Cauchon algorithm which has been proposed for finding a parameterization of the set of these matrices with a fixed pattern of nonvanishing minors is derived. The close connection of this variant to Neville elimination and bidiagonalization is shown and new determinantal tests for total nonnegativity are developed which require much fever minors to be tested than for the tests known so far. New characterizations of some subclasses of the totally nonnegative matrices as well as shorter proofs for some classes of matrices for being (nonsingular and) totally nonnegative are derived.
MSC-Klassifikation: 15A48
Fachgebiet (DDC): 510 Mathematik
Schlagwörter: Totally nonnegative matix, totally positive matrix, Cauchon algorithm, Neville elimination, bidiagonalization
Link zur Lizenz: Deposit-Lizenz
Universitätsbibliographie: Ja

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ADM, Mohammad, Jürgen GARLOFF, 2014. Improved tests and characterizations of totally nonnegative matrices. In: Electronic Journal of Linear Algebra (ELA). 27, pp. 588-610. ISSN 1081-3810. eISSN 1537-9582

@article{Adm2014Impro-29987, title={Improved tests and characterizations of totally nonnegative matrices}, year={2014}, doi={10.13001/1081-3810.1920}, volume={27}, issn={1081-3810}, journal={Electronic Journal of Linear Algebra (ELA)}, pages={588--610}, author={Adm, Mohammad and Garloff, Jürgen}, note={Article Number: 255} }

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