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Conference Papers Year : 2021

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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Dates and versions

hal-03274453 , version 1 (30-06-2021)
hal-03274453 , version 2 (23-07-2021)

Identifiers

  • HAL Id : hal-03274453 , version 2

Cite

Stef Graillat, Fabienne Jézéquel, Enzo Queiros Martins, Maxime Spyropoulos. Computing multiple roots of polynomials in stochastic arithmetic with Newton method and approximate GCD. International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC 2021), Dec 2021, Timisoara, Romania. ⟨hal-03274453v2⟩
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