A hybrid algorithm for multi-homogeneous Bézout number

DOI10.1016/j.amc.2006.12.053zbMath1122.65356OpenAlexW2026216848MaRDI QIDQ2383696

Heng Liang, Feng-Shan Bai, Yu-Hui Tao

Publication date: 19 September 2007

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

Full work available at URL: https://doi.org/10.1016/j.amc.2006.12.053

zbMATH Keywords

numerical examplespermanenthomotopy continuation methodhybrid algorithmmulti-homogeneous Bézout numberPolynomial systems

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)

Cites Work

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• The complexity of computing the permanent
• Random path method with pivoting for computing permanents of matrices
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• Computing all solutions to polynomial systems using homotopy continuation
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• Heuristic methods for computing the minimal multi-homogeneous Bézout number.
• Computing the optimal partition of variables in multi-homogeneous homotopy methods
• Minimizing multi-homogeneous Bézout numbers by a local search method
• A Monte-Carlo Algorithm for Estimating the Permanent
• Finding all solutions to polynomial systems and other systems of equations
• Optimization problem in multi-homogeneous homotopy method
• Two Algorithmic Results for the Traveling Salesman Problem

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