HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Journal articles

Dynamical control of Newton's method for multiple roots of polynomials

Abstract : In this article, we show how to perform a dynamical control of Newton's method for the computation of multiple roots of polynomials. Using Discrete Stochastic Arithmetic, root approximations are computed until the difference between two successive approximations is numerical noise. With such a stopping criterion, the optimal number of iterations in Newton's method are performed. Moreover it is possible to estimate in the result obtained which digits are in common with the exact root. Two strategies to estimate the multiplicity of polynomials roots are compared: one requires root approximations computed at different precisions and the other three successive iterates of Newton's method. We show that using such a strategy and then the modified Newton's method, multiple roots can be computed with a requested accuracy.
Document type :
Journal articles
Complete list of metadata

Cited literature [33 references]  Display  Hide  Download

Contributor : Fabienne Jezequel Connect in order to contact the contributor
Submitted on : Monday, September 12, 2016 - 10:43:17 AM
Last modification on : Saturday, May 21, 2022 - 3:52:36 AM
Long-term archiving on: : Tuesday, December 13, 2016 - 12:55:47 PM


Files produced by the author(s)


  • HAL Id : hal-01363961, version 1


Stef Graillat, Fabienne Jézéquel, Moustadrani Saïd Ibrahim. Dynamical control of Newton's method for multiple roots of polynomials. Reliable Computing Journal, 2016, 21. ⟨hal-01363961⟩



Record views


Files downloads