Zobrazeno 1 - 10
of 451
pro vyhledávání: '"14Q20"'
Autor:
Hilany, Boulos El, Tsigaridas, Elias
We present precise bit and degree estimates for the optimal value of the polynomial optimization problem $f^*:=\text{inf}_{x\in \mathscr{X}}~f(x)$, where $\mathscr{X}$ is a semi-algebraic set satisfying some non-degeneracy conditions. Our bounds depe
Externí odkaz:
http://arxiv.org/abs/2407.17093
Autor:
Burr, Michael, Byrd, Michael
We present a certified algorithm based on subdivision for computing an isotopic approximation to any number of curves in the plane. Our algorithm is based on the certified curve approximation algorithm of Plantinga and Vegter. The main challenge in t
Externí odkaz:
http://arxiv.org/abs/2407.16911
Autor:
Helmer, Martin, Mohr, Rafael
We describe a new algorithm to compute Whitney stratifications of real and complex algebraic varieties. This algorithm is a modification of the algorithm of Helmer and Nanda (HN), but is made more efficient by using techniques for equidimensional dec
Externí odkaz:
http://arxiv.org/abs/2406.17122
Autor:
Lombardi, Henri, Mahboubi, Assia
In this memoir, we seek to construct a dynamical theory as complete as possible to describe the algebraic properties of the field of real numbers in constructive mathematics without axiom of dependent choice. We propose a theory which turns out to be
Externí odkaz:
http://arxiv.org/abs/2406.15218
We present bounds for the geometric degree of the tangent bundle and the tangential variety of a smooth affine algebraic variety $V$ in terms of the geometric degree of $V$. We first analyze the case of curves, showing an explicit relation between th
Externí odkaz:
http://arxiv.org/abs/2403.10661
Autor:
Kreuzer, Martin, Robbiano, Lorenzo
Let $K$ be a field and $P=K[x_1,\dots,x_n]$. The technique of elimination by substitution is based on discovering a coherently $Z=(z_1,\dots,z_s)$-separating tuple of polynomials $(f_1,\dots,f_s)$ in an ideal $I$, i.e., on finding polynomials such th
Externí odkaz:
http://arxiv.org/abs/2403.06415
Autor:
La Valle, Chris, Tonelli-Cueto, Josué
Separation bounds are a fundamental measure of the complexity of solving a zero-dimensional system as it measures how difficult it is to separate its zeroes. In the positive dimensional case, the notion of reach takes its place. In this paper, we pro
Externí odkaz:
http://arxiv.org/abs/2402.15649
The study of the closest point(s) on a statistical model from a given distribution in the probability simplex with respect to a fixed Wasserstein metric gives rise to a polyhedral norm distance optimization problem. There are two components to the co
Externí odkaz:
http://arxiv.org/abs/2402.09626
The main results of this paper establish a partial correspondence between two previously-studied analogues of Groebner bases in the setting of algebras: namely, subalgebra (aka SAGBI) bases for quotients of polynomial rings and Khovanskii bases for v
Externí odkaz:
http://arxiv.org/abs/2402.06057
Dynamic models describe phenomena across scientific disciplines, yet to make these models useful in application the unknown parameter values of the models must be determined. Discrete-time dynamic models are widely used to model biological processes,
Externí odkaz:
http://arxiv.org/abs/2401.16220