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Mathematical Notes

, Volume 60, Issue 5, pp 503–509 | Cite as

Topological complexity and real roots of polynomials

  • V. A. Vassiliev
Article
  • 34 Downloads

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 degreed equalsd/2 for evend, is greater than or equal to 1 for oddd>−3, and equals 1 ford=3 or 5.

Key words

number of branchings of an algorithm topological complexity real roots of a polynomial approximate real root 

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References

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    V. A. Vassiliev, “Topological complexity of algorithms of approximate solution of systems of polynomial equations,”Algebra i Analiz,1, No. 6, 98–113 (1989).MathSciNetGoogle Scholar
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    V. A. Vassiliev,Complements of Discriminants of Smooth Maps: Topology and Applications, Revised edition. Translations of Math. Monographs, Vol. 98, Amer. Math. Soc., Providence, R.I. (1994).Google Scholar

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • V. A. Vassiliev
    • 1
    • 2
  1. 1.Russian Academy of SciencesV. A. Steklov Mathematics InstituteUSSR
  2. 2.Independent Moscow UniversityUSSR

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