Solving polynomial systems

DOI10.1007/BF03023953zbMath0637.65047MaRDI QIDQ1098563

Tien-Yien Li

Publication date: 1987

Published in: The Mathematical Intelligencer (Search for Journal in Brave)

zbMATH Keywords

Cauchy problempolynomial systemshomotopy continuation methodfour-dimensional Lorenz attractorrandom product homotopy

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Attractors and repellers of smooth dynamical systems and their topological structure (37C70)

Related Items (10)

Computing all nonsingular solutions of cyclic-\(n\) polynomial using polyhedral homotopy continuation methods ⋮ Analysis of Asymptotic Escape of Strict Saddle Sets in Manifold Optimization ⋮ PHoMpara-parallel implementation of the polyhedral homotopy continuation method for polynomial systems ⋮ Polynomial root finding by means of continuation ⋮ Improved estimation of defocus blur and spatial shifts in spatial domain: A homotopy-based approach. ⋮ A homotopy-based approach for computing defocus blur and affine transform simultaneously ⋮ Multiple-objective programming with polynomial objectives and constraints ⋮ A symmetric homotopy and hybrid polynomial system solving method for mixed trigonometric polynomial systems ⋮ The continuation method for rational and deficient systems ⋮ On decomposing systems of polynomial equations with finitely many solutions

Uses Software

• EISPACK

Cites Work

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• The local structure of a chaotic attractor in four dimensions
• A homotopy for solving polynomial systems
• Homotopy method for generalized eigenvalue problems \(Ax=\lambda Bx\)
• The random product homotopy and deficient polynomial systems
• Matrix eigensystem routines - EISPACK guide. 2nd ed
• Numerical Solution of a Class of Deficient Polynomial Systems
• Homotopy Method for General $\lambda $-Matrix Problems
• Simplicial and Continuation Methods for Approximating Fixed Points and Solutions to Systems of Equations
• On the Number of Solutions to Polynomial Systems of Equations
• Finding all solutions to polynomial systems and other systems of equations
• A homotopy method for eigenvalue assignment using decentralized state feedback

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