Computing multiple roots of polynomials in stochastic arithmetic with Newton method and approximate GCD
| Autor: | Graillat, Stef, Jézéquel, Fabienne, Queiros Martins, Enzo, Spyropoulos, Maxime |
|---|---|
| Přispěvatelé: | Performance et Qualité des Algorithmes Numériques (PEQUAN), LIP6, Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Université paris 2 Panthéon-Assas, JEZEQUEL, Fabienne, Plateforme d'analyse pour l'arithmétique flottante - - INTERFLOP2020 - ANR-20-CE46-0009 - AAPG2020 - VALID, ANR-20-CE46-0009,INTERFLOP,Plateforme d'analyse pour l'arithmétique flottante(2020) |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Discrete Stochastic Arithmetic
floating-point arithmetic [INFO.INFO-AO]Computer Science [cs]/Computer Arithmetic MathematicsofComputing_NUMERICALANALYSIS [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA] [INFO.INFO-NA]Computer Science [cs]/Numerical Analysis [cs.NA] approximate GCD Newton method [INFO.INFO-NA] Computer Science [cs]/Numerical Analysis [cs.NA] ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION rounding errors [INFO.INFO-AO] Computer Science [cs]/Computer Arithmetic numerical validation [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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