Homotopies for Intersecting Solution Components of Polynomial Systems

DOI10.1137/S0036142903430463zbMath1108.13308OpenAlexW2066058234MaRDI QIDQ4653921

Charles W. Wampler, Jan Verschelde, Andrew John Sommese

Publication date: 1 March 2005

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s0036142903430463

zbMATH Keywords

embeddinghomotopy continuationpolynomial systemirreducible componentsnumerical algebraic geometrycomponents of solutionsgeneric points

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Numerical computation of solutions to systems of equations (65H10) Polynomials, factorization in commutative rings (13P05) Computational aspects in algebraic geometry (14Q99)

Related Items (13)

An intrinsic homotopy for intersecting algebraic varieties ⋮ Cell decomposition of almost smooth real algebraic surfaces ⋮ Sampling algebraic sets in local intrinsic coordinates ⋮ Numerically computing real points on algebraic sets ⋮ Regenerative cascade homotopies for solving polynomial systems ⋮ Unification and extension of intersection algorithms in numerical algebraic geometry ⋮ Foreword. What is numerical algebraic geometry? ⋮ A hybrid symbolic-numerical approach to the center-focus problem ⋮ Numerical Decomposition of the Rank-Deficiency Set of a Matrix of Multivariate Polynomials ⋮ A homotopy method with adaptive basis selection for computing multiple solutions of differential equations ⋮ Regeneration homotopies for solving systems of polynomials ⋮ Numerical algebraic geometry and algebraic kinematics ⋮ The numerical algebraic geometry of bottlenecks

Uses Software

• PHCpack

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