Bézout number calculations for multi-homogeneous polynomial systems

DOI10.1016/0096-3003(92)90070-HzbMath0759.65023OpenAlexW2005936052MaRDI QIDQ1200228

Charles W. Wampler

Publication date: 17 January 1993

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

Full work available at URL: https://doi.org/10.1016/0096-3003(92)90070-h

zbMATH Keywords

homogenizationsBézout numbermulti- homogeneous continuationmulti-homogeneous system of polynomials

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Real polynomials: location of zeros (26C10)

Related Items (13)

Multihomogeneous resultant formulae by means of complexes ⋮ Symmetric homotopy construction ⋮ A convex geometric approach to counting the roots of a polynomial system ⋮ A hybrid algorithm for multi-homogeneous Bézout number ⋮ Mixed-volume computation by dynamic lifting applied to polynomial system solving ⋮ Heuristic methods for computing the minimal multi-homogeneous Bézout number. ⋮ Minimizing multi-homogeneous Bézout numbers by a local search method ⋮ Numerical Evidence for a Conjecture in Real Algebraic Geometry ⋮ Optimization problem in multi-homogeneous homotopy method ⋮ Computing the optimal partition of variables in multi-homogeneous homotopy methods ⋮ Incomplete Gröbner basis as a preconditioner for polynomial systems ⋮ Solving degenerate sparse polynomial systems faster ⋮ Toric intersection theory for affine root counting

Cites Work

• Solving systems of polynomial equations by bounded and real homotopy
• A homotopy for solving polynomial systems
• A homotopy for solving general polynomial systems that respects m- homogeneous structures
• Coefficient-parameter polynomial continuation
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