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Mat. Zametki, 1996, Volume 60, Issue 5, Pages 670–680 (Mi mz1880)  

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

Topological complexity and real roots of polynomials

V. A. Vassiliev

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: The topological complexity of an algorithm is the number of its branchings. In the paper we prove that the minimal topological complexity of an algorithm that approximately computes a root of a real polynomial of degree $d$ equals $d/2$ for even $d$, is greater than or equal to 1 for odd $d>-3$, and equals 1 for $d=3$ or 5.

DOI: https://doi.org/10.4213/mzm1880

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English version:
Mathematical Notes, 1996, 60:5, 503–509

Bibliographic databases:

UDC: 511
Received: 13.03.1996

Citation: V. A. Vassiliev, “Topological complexity and real roots of polynomials”, Mat. Zametki, 60:5 (1996), 670–680; Math. Notes, 60:5 (1996), 503–509

Citation in format AMSBIB
\Bibitem{Vas96}
\by V.~A.~Vassiliev
\paper Topological complexity and real roots of polynomials
\jour Mat. Zametki
\yr 1996
\vol 60
\issue 5
\pages 670--680
\mathnet{http://mi.mathnet.ru/mz1880}
\crossref{https://doi.org/10.4213/mzm1880}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1619889}
\zmath{https://zbmath.org/?q=an:0897.68055}
\transl
\jour Math. Notes
\yr 1996
\vol 60
\issue 5
\pages 503--509
\crossref{https://doi.org/10.1007/BF02309164}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1996WZ03000003}


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  • https://doi.org/10.4213/mzm1880
  • http://mi.mathnet.ru/eng/mz/v60/i5/p670

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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. V. A. Vassiliev, “On topological invariants of real algebraic functions”, Funct. Anal. Appl., 45:3 (2011), 163–172  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. V. A. Vassiliev, “Topological complexity and Schwarz genus of general real polynomial equation”, Mosc. Math. J., 11:3 (2011), 617–625  mathnet  mathscinet
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