A symmetric homotopy and hybrid polynomial system solving method for mixed trigonometric polynomial systems

DOI10.1090/S0025-5718-2013-02763-9zbMath1327.13102OpenAlexW2012797379MaRDI QIDQ5418491

Yan Yu, Bo Dong, Bo Yu

Publication date: 4 June 2014

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

Full work available at URL: https://doi.org/10.1090/s0025-5718-2013-02763-9

zbMATH Keywords

symmetryhomotopy methodpolynomial systemhybrid algorithmsymbolic-numeric computationmixed trigonometric polynomial system

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Numerical computation of solutions to systems of equations (65H10) Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Computational aspects in algebraic geometry (14Q99) Solving polynomial systems; resultants (13P15)

Related Items (3)

Efficiently counting affine roots of mixed trigonometric polynomial systems ⋮ The natural algorithmic approach of mixed trigonometric-polynomial problems ⋮ Polynomial Homotopy Method for the Sparse Interpolation Problem Part I: Equally Spaced Sampling

Uses Software

• HOM4PS
• PHCpack
• Bertini

Cites Work

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• HOM4PS-2.0: a software package for solving polynomial systems by the polyhedral homotopy continuation method
• A homotopy for solving polynomial systems
• A homotopy for solving general polynomial systems that respects m- homogeneous structures
• Computing all solutions to polynomial systems using homotopy continuation
• Solving polynomial systems
• The random product homotopy and deficient polynomial systems
• Coefficient-parameter polynomial continuation
• A new start system for solving deficient polynomial systems using continuation
• Symmetric homotopy construction
• Safe starting regions by fixed points and tightening
• Solving polynomial systems by polyhedral homotopies
• Symmetric Newton polytopes for solving sparse polynomial systems
• Numerical Solution of a Class of Deficient Polynomial Systems
• The Cheater’s Homotopy: An Efficient Procedure for Solving Systems of Polynomial Equations
• Regeneration homotopies for solving systems of polynomials
• Solving Deficient Polynomial Systems with Homotopies which Keep the Subschemes at Infinity Invariant
• A simple homotopy for solving deficient polynomial systems
• A Hybrid Polynomial System Solving Method for Mixed Trigonometric Polynomial Systems
• Finding All Solutions to a System of Polynomial Equations
• A Simple Homotopy Method for Determining all Isolated Solutions to Polynomial Systems
• Homotopies Exploiting Newton Polytopes for Solving Sparse Polynomial Systems
• Solving Polynomial Systems Using a Branch and Prune Approach
• Algorithm 795
• The $GBQ$-Algorithm for Constructing Start Systems of Homotopies for Polynomial Systems
• A Polyhedral Method for Solving Sparse Polynomial Systems

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