Zobrazeno 1 - 10
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pro vyhledávání: '"Imbach, Rémi"'
Autor:
Imbach, Rémi, Moroz, Guillaume
Evaluating or finding the roots of a polynomial $f(z) = f_0 + \cdots + f_d z^d$ with floating-point number coefficients is a ubiquitous problem. By using a piecewise approximation of $f$ obtained with a careful use of the Newton polygon of $f$, we im
Externí odkaz:
http://arxiv.org/abs/2302.06244
Autor:
Imbach, Rémi, Pan, Victor Y.
In our quest for the design, the analysis and the implementation of a subdivision algorithm for finding the complex roots of univariate polynomials given by oracles for their evaluation, we present sub-algorithms allowing substantial acceleration of
Externí odkaz:
http://arxiv.org/abs/2206.08622
Autor:
Imbach, Rémi, Pan, Victor Y.
We depart from our approximation of 2000 of all root radii of a polynomial, which has readily extended Sch{\"o}nhage's efficient algorithm of 1982 for a single root radius. We revisit this extension, advance it, based on our simple but novel idea, an
Externí odkaz:
http://arxiv.org/abs/2102.10821
Autor:
Imbach, Rémi, Pan, Victor Y.
We report an ongoing work on clustering algorithms for complex roots of a univariate polynomial $p$ of degree $d$ with real or complex coefficients. As in their previous best subdivision algorithms our root-finders are robust even for multiple roots
Externí odkaz:
http://arxiv.org/abs/1911.06706
Autor:
Imbach, Rémi, Pan, Victor Y.
We seek complex roots of a univariate polynomial $P$ with real or complex coefficients. We address this problem based on recent algorithms that use subdivision and have a nearly optimal complexity. They are particularly efficient when only roots in a
Externí odkaz:
http://arxiv.org/abs/1906.04920
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We describe Ccluster, a software for computing natural $\epsilon$-clusters of complex roots in a given box of the complex plane. This algorithm from Becker et al.~(2016) is near-optimal when applied to the benchmark problem of isolating all complex r
Externí odkaz:
http://arxiv.org/abs/1806.10584
This paper gives the first algorithm for finding a set of natural $\epsilon$-clusters of complex zeros of a triangular system of polynomials within a given polybox in $\mathbb{C}^n$, for any given $\epsilon>0$. Our algorithm is based on a recent near
Externí odkaz:
http://arxiv.org/abs/1806.10164
Functional iterations such as Newton's are a popular tool for polynomial root-finding. We consider realistic situation where some (e.g., better-conditioned) roots have already been approximated and where further computations is directed to approximat
Externí odkaz:
http://arxiv.org/abs/1606.01396
Autor:
Imbach, Rémi
We describe here the package {\tt subdivision\\_solver} for the mathematical software {\tt SageMath}. It provides a solver on real numbers for square systems of large dense polynomials. By large polynomials we mean multivariate polynomials with large
Externí odkaz:
http://arxiv.org/abs/1603.07916