Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/95694
Full metadata record
DC FieldValueLanguage
dc.contributor.authorKlerk, Etienne de.en
dc.contributor.authorPasechnik, Dmitrii V.en
dc.date.accessioned2012-07-03T01:48:21Zen
dc.date.accessioned2019-12-06T19:20:00Z-
dc.date.available2012-07-03T01:48:21Zen
dc.date.available2019-12-06T19:20:00Z-
dc.date.copyright2003en
dc.date.issued2003en
dc.identifier.citationKlerk, E. D., & Pasechnik, D. V. (2003). Products of positive forms, linear matrix inequalities, and Hilbert 17th problem for ternary forms. European Journal of Operational Research, 157(1), 39–45.en
dc.identifier.urihttps://hdl.handle.net/10356/95694-
dc.description.abstractA form p on Rn (homogeneous n-variate polynomial) is called positive semidefinite (p.s.d.) if it is nonnegative on Rn. In other words, the zero vector is a global minimizer of p in this case. The famous 17th conjecture of Hilbert [Bull. Amer. Math. Soc. (N.S.), 37 (4) (2000) 407] (later proven by Artin [The Collected Papers of Emil Artin, Addison-Wesley Publishing Co., Inc., Reading, MA, London, 1965]) is that a form p is p.s.d. if and only if it can be decomposed into a sum of squares of rational functions. In this paper we give an algorithm to compute such a decomposition for ternary forms (n = 3). This algorithm involves the solution of a series of systems of linear matrix inequalities (LMI's). In particular, for a given p.s.d. ternary form p of degree 2m, we show that the abovementioned decomposition can be computed by solving at most m/4 systems of LMI's of dimensions polynomial in m. The underlying methodology is largely inspired by the original proof of Hilbert, who had been able to prove his conjecture for the case of ternary forms.en
dc.format.extent13 p.en
dc.language.isoenen
dc.relation.ispartofseriesEuropean journal of operational researchen
dc.rights© 2003 Elsevier. This is the author created version of a work that has been peer reviewed and accepted for publication by European Journal of Operational Research, Elsevier. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: DOI [http://dx.doi.org/10.1016/j.ejor.2003.08.014].en
dc.subjectDRNTU::Science::Mathematics::Discrete mathematics::Theory of computationen
dc.titleProducts of positive forms, linear matrix inequalities, and Hilbert 17th problem for ternary formsen
dc.typeJournal Articleen
dc.contributor.schoolSchool of Physical and Mathematical Sciencesen
dc.identifier.doi10.1016/j.ejor.2003.08.014en
dc.description.versionAccepted versionen
item.fulltextWith Fulltext-
item.grantfulltextopen-
Appears in Collections:SPMS Journal Articles
Files in This Item:
File Description SizeFormat 
15.Products of positive forms.pdf433.37 kBAdobe PDFThumbnail
View/Open

SCOPUSTM   
Citations 50

4
Updated on Jan 17, 2021

PublonsTM
Citations 50

3
Updated on Jan 14, 2021

Page view(s) 50

431
Updated on Jan 17, 2021

Download(s) 5

389
Updated on Jan 17, 2021

Google ScholarTM

Check

Altmetric


Plumx

Items in DR-NTU are protected by copyright, with all rights reserved, unless otherwise indicated.