Conference abstracts

Plenary talk

July 15, 9:30 ~ 10:30

Finding one root of a polynomial system: Smale's 17th problem

Pierre Lairez

Inria, France   -

How many operations are sufficient to numerically compute one root of a polynomial system of equations? Smale's 17th problem asks whether a polynomial complexity is possible for random systems. We now have a thorough answer. Based on work by Beltrán, Bürgisser, Cucker, Pardo, Shub, Smale and myself, I will explain the main ideas that underlie it, from effective Newton's method estimates to the sampling of random system-solution pairs.

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FoCM 2017, based on a nodethirtythree design.