Toric Newton method for polynomial homotopies

DOI10.1006/jsco.1999.0296zbMath0992.65048OpenAlexW2023415027MaRDI QIDQ1569842

Jan Verschelde

Publication date: 28 September 2000

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/2550118788514fd3d3a03ab6f3ca658d167a56db

zbMATH Keywords

homogenizationscalingpolynomial systemssymbolic-numeric algorithmpolynomial homotopiestoric Newton method

Mathematics Subject Classification ID

Related Items (5)

Approximate Gröbner bases, overdetermined polynomial systems, and approximate GCDs ⋮ Deformation techniques to solve generalised Pham systems ⋮ Polyhedral homotopies in Cox coordinates ⋮ Tropical algebraic geometry in Maple: a preprocessing algorithm for finding common factors for multivariate polynomials with approximate coefficients ⋮ Random polynomials with prescribed Newton polytope

Uses Software

• HOMPACK90
• PHCpack
• HOMPACK

Cites Work

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• Errata: Coefficient-parameter polynomial continuation
• The number of roots of a system of equations
• Polyhedral end games for polynomial continuation
• A global view of residues in the torus
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• A methodology for solving chemical equilibrium systems
• Mixed-volume computation by dynamic lifting applied to polynomial system solving
• Algorithm 652
• The Cheater’s Homotopy: An Efficient Procedure for Solving Systems of Polynomial Equations
• Introduction to Toric Varieties. (AM-131)
• THE GEOMETRY OF TORIC VARIETIES
• Algorithm 777: HOMPACK90
• Homotopies Exploiting Newton Polytopes for Solving Sparse Polynomial Systems
• Lectures on Polytopes
• Algorithm 795
• A Polyhedral Method for Solving Sparse Polynomial Systems

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