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Journal Articles Foundations of Computational Mathematics Year : 2016

A deterministic algorithm to compute approximate roots of polynomial systems in polynomial average time

Pierre Lairez

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 Beltrán 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.
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Dates and versions

hal-01178588 , version 1 (20-07-2015)
hal-01178588 , version 2 (07-10-2015)
hal-01178588 , version 3 (19-05-2016)

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Pierre Lairez. A deterministic algorithm to compute approximate roots of polynomial systems in polynomial average time. Foundations of Computational Mathematics, 2016, ⟨10.1007/s10208-016-9319-7⟩. ⟨hal-01178588v3⟩
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