Related papers: Some results on inhomogeneous discriminants
In this paper, we study unirational differential curves and the corresponding differential rational parametrizations. We first investigate basic properties of proper differential rational parametrizations for unirational differential…
In this note we give a rational uniformisation equation of the discriminant loci associated to a non-degenerate affine complete intersection variety. To show this formula we establish a relation of the fibre-integral with the hypergeometric…
Given a unirational parameterization of a surface, we present a general algorithm to determine a birational parameterization without using parameterization algorithms. Additionally, if the surface is assumed to have a birational…
We propose a new approach for metric learning by framing it as learning a sparse combination of locally discriminative metrics that are inexpensive to generate from the training data. This flexible framework allows us to naturally derive…
We present first a brief review of the existing literature on shape optimization, stressing the recent use of Hamiltonian systems in topology optimization. In the second section, we collect some preliminaries on the implicit parametrization…
Recently, a method to compute the implicit equation of a parametrized hypersurface has been developed by the authors. We address here some questions related to this method. First, we prove that the degree estimate for the stabilization of…
A parameterized surface can be represented as a projection from a certain toric surface. This generalizes the classical homogeneous and bihomogeneous parameterizations. We extend to the toric case two methods for computing the implicit…
In this paper, we propose two new deterministic interpolation algorithms for a sparse multivariate polynomial given as a standard black-box by introducing new Kronecker type substitutions. Let $f\in \RB[x_1,\dots,x_n]$ be a sparse black-box…
An algorithm for the computation of global discrete conformal parametrizations with prescribed global holonomy signatures for triangle meshes was recently described in [Campen and Zorin 2017]. In this paper we provide a detailed analysis of…
We consider the problem of estimating log-determinants of large, sparse, positive definite matrices. A key focus of our algorithm is to reduce computational cost, and it is based on sparse approximate inverses. The algorithm can be…
We give an algorithm to compute inhomogeneous differential equations for definite integrals with parameters. The algorithm is based on the integration algorithm for $D$-modules by Oaku. Main tool in the algorithm is the Gr\"obner basis…
We present new, practical algorithms for the hypersurface implicitization problem: namely, given a parametric description (in terms of polynomials or rational functions) of the hypersurface, find its implicit equation. Two of them are for…
In this paper we describe an algorithm for implicitizing rational hypersurfaces in case there exists at most a finite number of base points. It is based on a technique exposed in math.AG/0210096, where implicit equations are obtained as…
In this paper, a method via sparse-sparse iteration for computing a sparse incomplete factorization of the inverse of a symmetric positive definite matrix is proposed. The resulting factorized sparse approximate inverse is used as a…
A (global) determinantal representation of hypersurface in P^n is a matrix, whose entries are linear forms in homogeneous coordinates and whose determinant defines the hypersurface. We study the properties of such representations for…
This paper investigates the stratification of the discriminant hypersurface associated with a univariate polynomial via the number of its distinct complex roots. We introduce two novel approaches different from the one based on…
We study a general class of convex submodular optimization problems with indicator variables. Many applications such as the problem of inferring Markov random fields (MRFs) with a sparsity or robustness prior can be naturally modeled in…
We present a matrix-based algorithm for deciding if the parametrization of a curve or a surface is invertible or not, and for computing the inverse of the parametrization if it exists.
This paper is concerned with the problem of approximating the determinant of A for a large sparse symmetric positive definite matrix A. It is shown that an efficient solution of this problem is obtained by using a sparse approximate inverse…
This paper investigates the idea of designing data-driven partial estimators for nonlinear systems showing parametric uncertainties using sparse multivariate polynomial relationships. A general framework is first presented and then…