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

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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Contributor : Pierre Lairez <>
Submitted on : Thursday, May 19, 2016 - 9:35:26 AM
Last modification on : Saturday, December 16, 2017 - 7:18:04 AM

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Pierre Lairez. A deterministic algorithm to compute approximate roots of polynomial systems in polynomial average time. Foundations of Computational Mathematics, Springer Verlag, 2016, ⟨http://link.springer.com/article/10.1007%2Fs10208-016-9319-7⟩. ⟨10.1007/s10208-016-9319-7⟩. ⟨hal-01178588v3⟩

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