Sweeping algebraic curves for singular solutions

DOI10.1016/j.cam.2009.07.056zbMath1189.65101arXiv0809.5281OpenAlexW2166284853MaRDI QIDQ970416

Jan Verschelde, Kathy Piret

Publication date: 17 May 2010

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

Full work available at URL: https://arxiv.org/abs/0809.5281

zbMATH Keywords

Newton's methodnumerical examplespolynomial systemdeflationsingular solutionpredictor-corrector methodspath followingquadratic turning pointssweeping homotopy

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) Real polynomials: location of zeros (26C10)

Related Items

Using monodromy to avoid high precision in homotopy continuation ⋮ A singular value homotopy for finding critical parameter values ⋮ A Robust Numerical Path Tracking Algorithm for Polynomial Homotopy Continuation ⋮ A Numerical Method for Computing Border Curves of Bi-parametric Real Polynomial Systems and Applications ⋮ Locating the closest singularity in a polynomial homotopy

Uses Software

• PHCpack
• RAGlib
• Taylor

Cites Work

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