Numerical root finding via Cox rings

DOI10.1016/j.jpaa.2020.106367zbMath1442.14187arXiv1903.12002OpenAlexW3013697203MaRDI QIDQ2173863

Simon Telen

Publication date: 17 April 2020

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.12002

zbMATH Keywords

toric varietiessystems of polynomial equationsCox ringmultiplication matrix

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Numerical solution of nonlinear eigenvalue and eigenvector problems (65H17) Numerical computation of roots of polynomial equations (65H04) Geometric aspects of numerical algebraic geometry (14Q65)

Related Items

Bayesian Integrals on Toric Varieties, Toric eigenvalue methods for solving sparse polynomial systems, Landau discriminants, Polyhedral homotopies in Cox coordinates, Koszul-Type Determinantal Formulas for Families of Mixed Multilinear Systems, Systems of Polynomial Equations, Higher-order Tensor Decompositions, and Multidimensional Harmonic Retrieval: A Unifying Framework. Part I: The Canonical Polyadic Decomposition

Uses Software

• Macaulay2
• PHCpack
• Bertini
• rootsb

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Multigraded Hilbert functions and toric complete intersection codes
• Irrational mixed decomposition and sharp fewnomial bounds for tropical polynomial systems
• Solving a sparse system using linear algebra
• Introduction to the solution of polynomial systems
• Polyhedral end games for polynomial continuation
• A global view of residues in the torus
• A stabilized normal form algorithm for generic systems of polynomial equations
• Solving polynomial equations. Foundations, algorithms, and applications
• Matrices in elimination theory
• Solving degenerate sparse polynomial systems faster
• Solving polynomial systems by polyhedral homotopies
• Multivariate polynomial equations with multiple zeros solved by matrix eigenproblems
• Stable normal forms for polynomial system solving
• Multigraded regularity: syzygies and fat points
• Polynomial Equations and Convex Polytopes
• Macaulay style formulas for sparse resultants
• Numerical Solution of Bivariate and Polyanalytic Polynomial Systems
• Numerical algebraic geometry and algebraic kinematics
• Introduction to Toric Varieties. (AM-131)
• Polymake and Lattice Polytopes
• Homotopies Exploiting Newton Polytopes for Solving Sparse Polynomial Systems
• Algorithm 795
• Toric residue and combinatorial degree
• Solving Polynomial Systems via Truncated Normal Forms
• Multigraded Castelnuovo-Mumford regularity
• A Polyhedral Method for Solving Sparse Polynomial Systems
• Towards Mixed Gröbner Basis Algorithms
• Gröbner Basis over Semigroup Algebras
• The Numerical Solution of Systems of Polynomials Arising in Engineering and Science