Condition pp 367-390 | Cite as

Smale’s 17th Problem: II

  • Peter Bürgisser
  • Felipe Cucker
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 349)


In the preceding chapter we described Smale’s 17th problem and a probabilistic solution for it, namely, a randomized algorithm whose average cost is polynomially bounded. Here we continue with this theme, adding further understanding of the behavior of the homotopy algorithm described in the previous chapter. Also, getting closer to the original formulation of Smale’s problem, this chapter exhibits a deterministic algorithm whose average cost is nearly polynomial.


Average Cost Conditional Density Deterministic Algorithm Gaussian Density Approximate Zero 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Peter Bürgisser
    • 1
  • Felipe Cucker
    • 2
  1. 1.Institut für MathematikTechnische Universität BerlinBerlinGermany
  2. 2.Department of MathematicsCity University of Hong KongHong KongHong Kong SAR

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