@unpublished{L-A-Deterministic-Algorithm-To-Compute-Approximate-Roots-Of-Polynomial-Systems-In-Polynomial-Average-Time,
Title = {A deterministic algorithm to compute approximate roots of polynomial systems in polynomial average time},
Author = {Pierre Lairez},
Year = {2015},
Month = {10},
Note = {To appear in Foundations of computational mathematics (2016), 23 pages.},
Abstract = {We describe a deterministic algorithm that computes an approximate root of n complex polynomial equations in n unknowns in average polynomial time with respect to the size of the input, in the Blum-Shub-Smale model with square root. It rests upon a derandomization of an algorithm of Beltr\´an and Pardo and gives a deterministic affirmative answer to Smale's 17th problem. The main idea is to make use of the randomness contained in the input itself.},
Url = {http://arxiv.org/abs/1507.05485}
}