Counting solutions of a polynomial system locally and exactly

Autor: Ruben Becker, Michael Sagraloff

Publikováno v: Journal of Symbolic Computation. 120:102222

We propose a symbolic-numeric algorithm to count the number of solutions of a polynomial system within a local region. More specifically, given a zero-dimensional system $f_1=\cdots=f_n=0$, with $f_i\in\mathbb{C}[x_1,\ldots,x_n]$, and a polydisc $\ma

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d50fb9521625e5c49339102763e56d9c
https://doi.org/10.1016/j.jsc.2023.102222

Solving bivariate systems using Rational Univariate Representations

Autor: Fabrice Rouillier, Guillaume Moroz, Michael Sagraloff, Sylvain Lazard, Yacine Bouzidi, Marc Pouget

Publikováno v: Journal of Complexity
Journal of Complexity, Elsevier, 2016, 37, pp.34--75. ⟨10.1016/j.jco.2016.07.002⟩
Journal of Complexity, 2016, 37, pp.34--75. ⟨10.1016/j.jco.2016.07.002⟩

International audience; Given two coprime polynomials $P$ and $Q$ in $\Z[x,y]$ of degree bounded by $d$ and bitsize bounded by $\tau$, we address the problem of solving the system $\{P,Q\}$. We are interested in certified numerical approximations or,

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1aab2c63df0d23d9f0cf7c4832faab22
https://doi.org/10.1016/j.jco.2016.07.002

Root refinement for real polynomials using quadratic interval refinement

Autor: Michael Kerber, Michael Sagraloff

Publikováno v: Journal of Computational and Applied Mathematics. 280:377-395

We consider the problem of approximating all real roots of a square-free polynomial f with real coefficients. Given isolating intervals for the real roots and an arbitrary positive integer L , the task is to approximate each root to L bits after the

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::d9f24aa6c551cad52164494db20b7523
https://doi.org/10.1016/j.cam.2014.11.031

On the complexity of the Descartes method when using approximate arithmetic

Autor: Michael Sagraloff

Publikováno v: Journal of Symbolic Computation. 65:79-110

In this paper, we introduce a variant of the Descartes method to isolate the real roots of a square-free polynomial F ( x ) = ∑ i = 0 n A i x i with arbitrary real coefficients. It is assumed that each coefficient of F can be approximated to any sp

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::65bf5c52c344be57d11178753f2fe981
https://doi.org/10.1016/j.jsc.2014.01.005

Computing Real Roots of Real Polynomials ... and now For Real!

Autor: Michael Sagraloff, Alexander Kobel, Fabrice Rouillier

Publikováno v: ISSAC '16 Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation
ISSAC '16 Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation, Jul 2016, Waterloo, Canada. pp.7, ⟨10.1145/2930889.2930937⟩
ISSAC

Very recent work introduces an asymptotically fast subdivision algorithm, denoted ANewDsc, for isolating the real roots of a univariate real polynomial. The method combines Descartes' Rule of Signs to test intervals for the existence of roots, Newton

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5bb97a888d6ef582dadea56a16e1f541
https://hal.inria.fr/hal-01363955