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FOCM
2008

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

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On Smale's 17th Problem: A Probabilistic Positive Solution
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 17th Problem.
Carlos Beltrán, Luis Miguel Pardo
Added 10 Dec 2010
Updated 10 Dec 2010
Type Journal
Year 2008
Where FOCM
Authors Carlos Beltrán, Luis Miguel Pardo
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