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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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https://hal.archives-ouvertes.fr/hal-01178588
Contributor : Pierre Lairez <>
Submitted on : Wednesday, October 7, 2015 - 3:24:14 PM
Last modification on : Monday, December 28, 2020 - 10:22:04 AM
Long-term archiving on: : Friday, January 8, 2016 - 10:43:08 AM

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  • HAL Id : hal-01178588, version 2

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Pierre Lairez. A deterministic algorithm to compute approximate roots of polynomial systems in polynomial average time. 2015. ⟨hal-01178588v2⟩

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