The random product homotopy and deficient polynomial systems

DOI10.1007/BF01400351zbMath0656.65055MaRDI QIDQ1110271

James A. Yorke, Timothy Sauer, Tien-Yien Li

Publication date: 1987

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133208

zbMATH Keywords

polynomial systemshomotopy continuation methodcontinuation methodshomotopy methodsstructure at infinityisolated solutionsrandom product homotopydeficient systemsm-homogeneous technique

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Real polynomials: location of zeros (26C10) Numerical solution of nonlinear eigenvalue and eigenvector problems (65H17)

Related Items (10)

Homotopies for solving polynomial systems within a bounded domain ⋮ Solving polynomial systems ⋮ A simple homotopy for solving deficient polynomial systems ⋮ Polynomial root finding by means of continuation ⋮ Unmixing the mixed volume computation ⋮ Efficiently counting affine roots of mixed trigonometric polynomial systems ⋮ Minimizing multi-homogeneous Bézout numbers by a local search method ⋮ A symmetric homotopy and hybrid polynomial system solving method for mixed trigonometric polynomial systems ⋮ The BKK root count in $\mathbf {C}^n$ ⋮ Symmetric homotopy method for discretized elliptic equations with cubic and quintic nonlinearities

Uses Software

• HOMPACK

Cites Work

• The local structure of a chaotic attractor in four dimensions
• A homotopy for solving polynomial systems
• Homotopy method for generalized eigenvalue problems \(Ax=\lambda Bx\)
• Numerical Solution of a Class of Deficient Polynomial Systems
• Algorithm 652
• Finding All Solutions to a System of Polynomial Equations
• Homotopy Method for General $\lambda $-Matrix Problems
• Simplicial and Continuation Methods for Approximating Fixed Points and Solutions to Systems of Equations
• On Steplength Algorithms for a Class of Continuation Methods
• Finding all solutions to polynomial systems and other systems of equations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: The random product homotopy and deficient polynomial systems