Related papers: Reduction-Based Creative Telescoping for Algebraic…
Statistics and Optimization are foundational to modern Machine Learning. Here, we propose an alternative foundation based on Abstract Algebra, with mathematics that facilitates the analysis of learning. In this approach, the goal of the…
Many computer vision applications require robust and efficient estimation of camera geometry from a minimal number of input data measurements, i.e., solving minimal problems in a RANSAC framework. Minimal problems are usually formulated as…
This paper focuses on symbolic integration of differential forms, with a particular emphasis on historical and modern developments, from Abel's addition theorems for Abelian integrals to Zeilberger's creative telescoping for parameterized…
We discuss algorithms for arithmetic properties of hypergeometric functions. Most notably, we are able to compute the p-adic valuation of a hypergeometric function on any disk of radius smaller than the p-adic radius of convergence. This we…
We consider multidimensional optimization problems, which are formulated and solved in terms of tropical mathematics. The problems are to minimize (maximize) a linear or nonlinear function defined on vectors over an idempotent semifield,…
The aim of this paper is to construct sup-exponentially localized kernels and frames in the context of classical orthogonal expansions, namely, expansions in Jacobi polynomials, spherical harmonics, orthogonal polynomials on the ball and…
We present an algorithm which computes a cylindrical algebraic decomposition of a semialgebraic set using projection sets computed for each cell separately. Such local projection sets can be significantly smaller than the global projection…
Hyperbolic programming is the problem of computing the infimum of a linear function when restricted to the hyperbolicity cone of a hyperbolic polynomial, a generalization of semidefinite programming. We propose an approach based on symbolic…
This paper presents an algorithmic framework for the minimization of strictly convex quadratic functions. The framework is flexible and generic. At every iteration the search direction is a linear combination of the negative gradient, as…
In this paper, we extend a recently established subgradient method for the computation of Riemannian metrics that optimizes certain singular value functions associated with dynamical systems. This extension is threefold. First, we introduce…
We develop numerical homotopy algorithms for solving systems of polynomial equations arising from the classical Schubert calculus. These homotopies are optimal in that generically no paths diverge. For problems defined by hypersurface…
Low-rank tensor approximation techniques attempt to mitigate the overwhelming complexity of linear algebra tasks arising from high-dimensional applications. In this work, we study the low-rank approximability of solutions to linear systems…
A relaxation method based on border basis reduction which improves the efficiency of Lasserre's approach is proposed to compute the optimum of a polynomial function on a basic closed semi algebraic set. A new stopping criterion is given to…
Discrete tomography is concerned with the reconstruction of images that are defined on a discrete set of lattice points from their projections in several directions. The range of values that can be assigned to each lattice point is…
This study proposes an intrusive projection-based model-order reduction framework for nonlinear problems with a polynomial structure, solved iteratively using a Newton solver in the reduced space. It is demonstrated that for the targeted…
We propose a new method for constructing elimination templates for efficient polynomial system solving of minimal problems in structure from motion, image matching, and camera tracking. We first construct a particular affine…
The (efficient and parsimonious) decomposition of higher-order tensors is a fundamental problem with numerous applications in a variety of fields. Several methods have been proposed in the literature to that end, with the Tucker and PARAFAC…
In this paper, we propose an incremental algorithm for computing cylindrical algebraic decompositions. The algorithm consists of two parts: computing a complex cylindrical tree and refining this complex tree into a cylindrical tree in real…
We encode the binomials belonging to the toric ideal $I_A$ associated with an integral $d \times n$ matrix $A$ using a short sum of rational functions as introduced by Barvinok \cite{bar,newbar}. Under the assumption that $d,n$ are fixed,…
This paper introduces a strategy for signature-based algorithms to compute Groebner basis. The signature-based algorithms generate S-pairs instead of S-polynomials, and use s-reduction instead of the usual reduction used in the Buchberger…