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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Foundations of Computational Mathematics, Springer Verlag, 2016, <http://link.springer.com/article/10.1007%2Fs10208-016-9319-7>. <10.1007/s10208-016-9319-7>
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https://hal.archives-ouvertes.fr/hal-01178588
Contributeur : Pierre Lairez <>
Soumis le : jeudi 19 mai 2016 - 09:35:26
Dernière modification le : samedi 21 mai 2016 - 01:01:28

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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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