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Computing multiple roots of polynomials in stochastic arithmetic with Newton method and approximate GCD

Abstract : In this article, we propose new methods to compute multiple roots of polynomials in floating-point arithmetic. We rely on stochastic arithmetic that makes it possible to deal with rounding errors. We develop the concept of stochastic GCD that we use to deflate a polynomial in order to obtain a polynomial with single roots. We can then apply Newton method to get fast and accurate approximations of the roots. Numerical experiments show the effectiveness and efficiency of our methods.
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https://hal.archives-ouvertes.fr/hal-03274453
Contributor : Fabienne Jezequel <>
Submitted on : Friday, July 23, 2021 - 4:18:32 PM
Last modification on : Thursday, July 29, 2021 - 4:02:31 AM

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article_Newton_GCD_v2.pdf
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  • HAL Id : hal-03274453, version 2

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Stef Graillat, Fabienne Jézéquel, Enzo Queiros Martins, Maxime Spyropoulos. Computing multiple roots of polynomials in stochastic arithmetic with Newton method and approximate GCD. 2021. ⟨hal-03274453v2⟩

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