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 metadatas

Cited literature [33 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01363961
Contributor : Fabienne Jezequel <>
Submitted on : Monday, September 12, 2016 - 10:43:17 AM
Last modification on : Thursday, March 21, 2019 - 2:22:30 PM
Long-term archiving on : Tuesday, December 13, 2016 - 12:55:47 PM

File

article_HAL.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01363961, version 1

Citation

Stef Graillat, Fabienne Jézéquel, Moustadrani Saïd Ibrahim. Dynamical control of Newton's method for multiple roots of polynomials. Reliable Computing Journal, 2016, 21, ⟨http://interval.louisiana.edu/reliable-computing-journal/volume-21/reliable-computing-21-pp-117-139.pdf⟩. ⟨hal-01363961⟩

Share

Metrics

Record views

201

Files downloads

540