Heuristic methods for computing the minimal multi-homogeneous Bézout number.

DOI10.1016/S0096-3003(02)00540-4zbMath1044.65042MaRDI QIDQ1412521

Zhenjiang Lin, Ting Li, Feng-Shan Bai

Publication date: 25 November 2003

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

zbMATH Keywords

continuation methodsystem of polynomial equationsmulti-homogeneous Bézout number

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) Complexity and performance of numerical algorithms (65Y20)

Related Items (3)

A hybrid algorithm for multi-homogeneous Bézout number ⋮ Optimization problem in multi-homogeneous homotopy method ⋮ Computing the optimal partition of variables in multi-homogeneous homotopy methods

Uses Software

• Genocop

Cites Work

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• Bernstein's theorem in affine space
• A homotopy for solving general polynomial systems that respects m- homogeneous structures
• Bézout number calculations for multi-homogeneous polynomial systems
• Eine Methode zur Berechnung sämtlicher Lösungen von Polynomgleichungssystemen
• Finding all isolated zeros of polynomial systems in \(\mathbb{C}^n\) via stable mixed volumes
• Mixed-volume computation by dynamic lifting applied to polynomial system solving
• Minimizing multi-homogeneous Bézout numbers by a local search method
• Finding all solutions to polynomial systems and other systems of equations
• A Polyhedral Method for Solving Sparse Polynomial Systems

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