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Matematicheskie Zametki, 2002, Volume 71, Issue 1, Pages 27–36
DOI: https://doi.org/10.4213/mzm325 (Mi mzm325) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Positive Quadratic Forms on Intersections of Quadrics

A. V. Arutyunov

Peoples Friendship University of Russia
Full-text PDF (201 kB) Citations (5)
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DOI: https://doi.org/10.4213/mzm325
Abstract: The positive definiteness of a quadratic form on the cone defined as the set of points at which given quadratic forms vanish or are nonnegative is studied. Necessary and sufficient conditions for the positivity of a quadratic form on this cone are obtained. The results are applied to study second-order sufficient conditions for abnormal extremal problems.
Received: 30.08.2000
English version:
Mathematical Notes, 2002, Volume 71, Issue 1, Pages 25–33
DOI: https://doi.org/10.1023/A:1013918105631
Bibliographic databases:
UDC: 517.9
Language: Russian
Citation: A. V. Arutyunov, “Positive Quadratic Forms on Intersections of Quadrics”, Mat. Zametki, 71:1 (2002), 27–36; Math. Notes, 71:1 (2002), 25–33
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/mzm325
  • https://doi.org/10.4213/mzm325
  • https://www.mathnet.ru/eng/mzm/v71/i1/p27
    • This publication is cited in the following 5 articles:
    1. A. V. Arutyunov, S. E. Zhukovskiy, “On the Second Order Sufficient Optimality Conditions for a Problem of Mathematical Programming”, Math. Notes, 115:2 (2024), 148–163  mathnet  crossref  crossref  mathscinet
    2. Ganikhodzhaev R. Mukhamedov F. Saburov M., “Elliptic Quadratic Operator Equations”, Acta Appl. Math., 159:1 (2019), 29–74  crossref  mathscinet  isi  scopus
    3. A. V. Arutyunov, “Smooth abnormal problems in extremum theory and analysis”, Russian Math. Surveys, 67:3 (2012), 403–457  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. Meurant G., “The Complete Stagnation of Gmres for N <= 4”, Electron. Trans. Numer. Anal., 39 (2012), 75–101  mathscinet  zmath  isi  elib
    5. A. V. Arutyunov, “Nonnegativity of Quadratic Forms on Intersections of Quadrics and Quadratic Maps”, Math. Notes, 84:2 (2008), 155–165  mathnet  crossref  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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