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Computing Multiple Roots of Polynomials in Stochastic Arithmetic with Newton Method and Approximate GCD

EasyChair Preprint 7184

7 pagesDate: December 7, 2021

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.

Keyphrases: Approximate GCD, Discrete Stochastic Arithmetic, Newton method, floating-point arithmetic, numerical validation, rounding errors

BibTeX entry
BibTeX does not have the right entry for preprints. This is a hack for producing the correct reference:
@booklet{EasyChair:7184,
  author    = {Stef Graillat and Fabienne Jézéquel and Enzo Queiros Martins and Maxime Spyropoulos},
  title     = {Computing Multiple Roots of Polynomials in Stochastic Arithmetic with Newton Method and Approximate GCD},
  howpublished = {EasyChair Preprint 7184},
  year      = {EasyChair, 2021}}
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