Certifying zeros of polynomial systems using interval arithmetic
We establish interval arithmetic as a practical tool for certification in numerical algebraic
geometry. Our software HomotopyContinuation. jl now has a built-in function certify, which …
geometry. Our software HomotopyContinuation. jl now has a built-in function certify, which …
GPU-based homotopy continuation for minimal problems in computer vision
Abstract Systems of polynomial equations arise frequently in computer vision, especially in
multiview geometry problems. Traditional methods for solving these systems typically aim to …
multiview geometry problems. Traditional methods for solving these systems typically aim to …
Adjoints and canonical forms of polypols
Polypols are natural generalizations of polytopes, with boundaries given by nonlinear
algebraic hypersurfaces. We describe polypols in the plane and in 3-space that admit a …
algebraic hypersurfaces. We describe polypols in the plane and in 3-space that admit a …
The (block) Macaulay matrix: Solving systems of multivariate polynomial equations and multiparameter eigenvalue problems
C Vermeersch, B De Moor - 2023 - lirias.kuleuven.be
One of the most pervasive tools from (numerical) linear algebra is, without any doubt, the
standard eigenvalue decomposition. Eigenvalues describe the intrinsic system dynamics of …
standard eigenvalue decomposition. Eigenvalues describe the intrinsic system dynamics of …
[HTML][HTML] Hilbert functions of chopped ideals
A chopped ideal is obtained from a homogeneous ideal by considering only the generators
of a fixed degree. We investigate cases in which the chopped ideal defines the same finite …
of a fixed degree. We investigate cases in which the chopped ideal defines the same finite …
Solving sparse polynomial systems using Groebner bases and resultants
MR Bender - Proceedings of the 2022 International Symposium on …, 2022 - dl.acm.org
Solving systems of polynomial equations is a central problem in nonlinear and
computational algebra. Since Buchberger's algorithm for computing Gröbner bases in the …
computational algebra. Since Buchberger's algorithm for computing Gröbner bases in the …
[PDF][PDF] Solving Polynomial Equations and Applications
S Telen - CoRR, 2022 - event.cwi.nl
These notes accompany an introductory lecture given by the author at the workshop on
solving polynomial equations & applications at CWI Amsterdam in the context of the 2022 …
solving polynomial equations & applications at CWI Amsterdam in the context of the 2022 …
Toric Sylvester forms
L Busé, C Checa - Journal of Pure and Applied Algebra, 2024 - Elsevier
In this paper, we investigate the structure of the saturation of ideals generated by sparse
homogeneous polynomials over a projective toric variety X with respect to the irrelevant …
homogeneous polynomials over a projective toric variety X with respect to the irrelevant …
Sparse resultant-based methods with their applications to generalized cameras
S Bhayani - 2023 - oulurepo.oulu.fi
This thesis studies sparse resultants for solving polynomial systems with a view towards
camera geometry problems in computer vision. These problems are typically modeled as …
camera geometry problems in computer vision. These problems are typically modeled as …
Polynomial Equations: Theory and Practice
S Telen - Polynomial Optimization, Moments, and Applications, 2023 - Springer
Solving polynomial equations is a subtask of polynomial optimization. This chapter
introduces systems of such equations and the main approaches for solving them. We …
introduces systems of such equations and the main approaches for solving them. We …