An a posteriori certification algorithm for Newton homotopies

DOI10.1145/2608628.2608651zbMath1325.65074OpenAlexW2093973500MaRDI QIDQ3452402

Ian Haywood, Jonathan D. Hauenstein, Alan C. jun. Liddell

Publication date: 11 November 2015

Published in: Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1145/2608628.2608651

zbMATH Keywords

homotopy continuationalpha theoryalphacertifiedcertified trackingNewton homotopy

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Artificial intelligence for robotics (68T40) Solving polynomial systems; resultants (13P15)

Related Items

On the equations defining some Hilbert schemes ⋮ A primal-dual formulation for certifiable computations in Schubert calculus ⋮ Certifying solutions to overdetermined and singular polynomial systems over \(\mathbb{Q}\) ⋮ Using monodromy to recover symmetries of polynomial systems ⋮ Certified predictor-corrector tracking for Newton homotopies ⋮ Numerical computation of Galois groups ⋮ Foreword. What is numerical algebraic geometry? ⋮ Mixed cell computation in HOM4ps ⋮ Computing complex and real tropical curves using monodromy ⋮ Using monodromy to statistically estimate the number of solutions ⋮ On Computing the Nonlinearity Interval in Parametric Semidefinite Optimization

Uses Software

• Jordan

Cites Work

• Unnamed Item
• Unnamed Item
• An effective implementation of symbolic-numeric cylindrical algebraic decomposition for quantifier elimination
• Cylindrical algebraic decomposition using validated numerics
• The Jordan Curve Theorem, Formally and Informally
• On Computable Numbers, with an Application to the Entscheidungsproblem
• Definability and decision problems in arithmetic

This page was built for publication: An a posteriori certification algorithm for Newton homotopies