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Foundations of Computational Mathematics

, Volume 8, Issue 1, pp 1–43 | Cite as

On Smale's 17th Problem: A Probabilistic Positive Solution

  • Carlos Beltran
  • Luis Miguel Pardo
Article

Abstract

Smale's 17th Problem asks “Can a zero of n complex polynomial equations in n unknowns be found approximately, on the average [for a suitable probability measure on the space of inputs], in polynomial time with a uniform algorithm?” We present a uniform probabilistic algorithm for this problem and prove that its complexity is polynomial. We thus obtain a partial positive solution to Smale's 17th Problem.

Keywords

Positive Real Number Polynomial System Coarea Formula Approximate Zero Initial Pair 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Society for Foundations of Computational Mathematics 2007

Authors and Affiliations

  1. 1.Departamento de Matematicas, Estadistica y Computacion, F. de Ciencias, University of CantabriaE-39071 SantanderSpain

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