Symmetric homotopy construction

DOI10.1016/0377-0427(94)90329-8zbMath0806.65055OpenAlexW2024630469WikidataQ57779005 ScholiaQ57779005MaRDI QIDQ1334800

Ronald Cools, Jan Verschelde

Publication date: 22 September 1994

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0377-0427(94)90329-8

zbMATH Keywords

symmetryorbitgroupsystem of polynomial equationscomplex solutionsnumber of homotopy pathsnumerical homotopy continuation methods

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15)

Related Items (7)

Homotopies for solving polynomial systems within a bounded domain ⋮ Computing Geometric Feature Sizes for Algebraic Manifolds ⋮ A Robust Numerical Path Tracking Algorithm for Polynomial Homotopy Continuation ⋮ A symmetric homotopy and hybrid polynomial system solving method for mixed trigonometric polynomial systems ⋮ A homotopy perturbation method for solving a neutron transport equation ⋮ Polynomial Homotopy Method for the Sparse Interpolation Problem Part I: Equally Spaced Sampling ⋮ Symmetric homotopy method for discretized elliptic equations with cubic and quintic nonlinearities

Uses Software

• HOMPACK

Cites Work

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• Globally convergent homotopy methods: A tutorial
• Solving systems of polynomial equations by bounded and real homotopy
• A homotopy for solving polynomial systems
• A homotopy for solving general polynomial systems that respects m- homogeneous structures
• Coefficient-parameter polynomial continuation
• A new start system for solving deficient polynomial systems using continuation
• Nonlinear reduction for solving deficient polynomial systems by continuation methods
• Bézout number calculations for multi-homogeneous polynomial systems
• Symbolic homotopy construction
• Numerical Solution of a Class of Deficient Polynomial Systems
• Algorithm 652
• A simple homotopy for solving deficient polynomial systems
• A Method for Computing All Solutions to Systems of Polynomials Equations
• Finding all isolated solutions to polynomial systems using HOMPACK
• The $GBQ$-Algorithm for Constructing Start Systems of Homotopies for Polynomial Systems
• A Neural Network Modeled by an Adaptive Lotka-Volterra System

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