Certifying zeros of polynomial systems using interval arithmetic

DOI10.1145/3580277MaRDI QIDQ6600004

Kemal Rose, Sascha Timme, Paul Breiding

Publication date: 6 September 2024

Published in: ACM Transactions on Mathematical Software (Search for Journal in Brave)

zbMATH Keywords

datasetsneural networksgaze detectiontext tagging

Mathematics Subject Classification ID

Numerical analysis (65-XX)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Interval analysis and automatic result verification
• Coefficient-parameter polynomial continuation
• HomotopyContinuation.jl: a package for homotopy continuation in Julia
• Application of interval Newton's method to chemical engineering problems
• Likelihood equations and scattering amplitudes
• Equations for GL invariant families of polynomials
• Numerical algebraic geometry
• Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken
• Hom4PS-3: A Parallel Numerical Solver for Systems of Polynomial Equations Based on Polyhedral Homotopy Continuation Methods
• Verification methods: Rigorous results using floating-point arithmetic
• Julia: A Fresh Approach to Numerical Computing
• Algorithm 921
• A Test for Existence of Solutions to Nonlinear Systems
• Algorithm 795
• Arb: Efficient Arbitrary-Precision Midpoint-Radius Interval Arithmetic
• Accuracy and Stability of Numerical Algorithms
• A Polyhedral Method for Solving Sparse Polynomial Systems
• Tangent Quadrics in Real 3-Space
• Nodes on quintic spectrahedra
• Exploiting symmetry in the power flow equations using monodromy
• Effective Certification of Approximate Solutions to Systems of Equations Involving Analytic Functions
• 3264 Conics in a Second
• The Numerical Solution of Systems of Polynomials Arising in Engineering and Science
• Solving polynomial systems via homotopy continuation and monodromy
• Certifying approximate solutions to polynomial systems on Macaulay2

Related Items (6)

Implementing real polyhedral homotopy ⋮ Computing algebraic degrees of phylogenetic varieties ⋮ Solving the area-length systems in discrete gravity using homotopy continuation ⋮ Principal Landau determinants ⋮ Recovery of plane curves from branch points ⋮ Effective alpha theory certification using interval arithmetic: alpha theory over regions

This page was built for publication: Certifying zeros of polynomial systems using interval arithmetic