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Diskretn. Anal. Issled. Oper., 2013, Volume 20, Number 3, Pages 65–70 (Mi da732)  

This article is cited in 2 scientific papers (total in 2 papers)

On monomials in quadratic forms

A. V. Seliverstov

Kharkevich Institute for Information Transmision Problems RAS, 19 build. 1, Bolshoy Karetny Lane, 127994 Moscow, Russia

Abstract: There are proved some restrictions on the zero-nonzero pattern of entries in a matrix of the real quadratic form which reaches its minimum value on a large set of vertices of the multidimensional cube centered at the origin whose edges are parallel to the coordinate axes. In particular, if the graph of the matrix contains an articulation point then the set of minima of the corresponding quadratic form is not maximal (with respect to set inclusion) among all such sets for various quadratic forms. Bibliogr. 21.

Keywords: combinatorial optimization, quadratic form, polytope, facet, graph, matrix.

Full text: PDF file (225 kB)
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English version:
Journal of Applied and Industrial Mathematics, 2013, 7:3, 431–434

Bibliographic databases:

Document Type: Article
UDC: 514.172.45
Received: 28.06.2012
Revised: 10.01.2013

Citation: A. V. Seliverstov, “On monomials in quadratic forms”, Diskretn. Anal. Issled. Oper., 20:3 (2013), 65–70; J. Appl. Industr. Math., 7:3 (2013), 431–434

Citation in format AMSBIB
\Bibitem{Sel13}
\by A.~V.~Seliverstov
\paper On monomials in quadratic forms
\jour Diskretn. Anal. Issled. Oper.
\yr 2013
\vol 20
\issue 3
\pages 65--70
\mathnet{http://mi.mathnet.ru/da732}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3135744}
\transl
\jour J. Appl. Industr. Math.
\yr 2013
\vol 7
\issue 3
\pages 431--434
\crossref{https://doi.org/10.1134/S1990478913030162}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. V. Seliverstov, “Mnogogranniki i svyaznye podgrafy”, Diskretn. analiz i issled. oper., 21:3 (2014), 82–86  mathnet  mathscinet
    2. A. B. Sviridenko, “Pryamye multiplikativnye metody dlya razrezhennykh matrits. Nyutonovskie metody”, Kompyuternye issledovaniya i modelirovanie, 9:5 (2017), 679–703  mathnet  crossref
  • Дискретный анализ и исследование операций
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