Incomplete Gröbner basis as a preconditioner for polynomial systems

DOI10.1016/j.cam.2008.05.054zbMath1165.65026OpenAlexW2091193233MaRDI QIDQ1008653

Feng-Shan Bai, Yu-Hui Tao, Yang Sun

Publication date: 30 March 2009

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

Full work available at URL: https://doi.org/10.1016/j.cam.2008.05.054

zbMATH Keywords

homotopy continuationpreconditionerdegree reductionBézout numberdeficient nonlinear algebraic systemincomplete Gröbner basis (IGB)PHCpackS-polynomialssubtraction polynomialtruncated Gröbner basis

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) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Real polynomials: location of zeros (26C10)

Uses Software

• PHCpack
• PoSSo

Cites Work

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• Coefficient-parameter polynomial continuation
• Mathematical reduction of a heart dipole model
• A new start system for solving deficient polynomial systems using continuation
• The membership problem for unmixed polynomial ideals is solvable in single exponential time
• Nonlinear reduction for solving deficient polynomial systems by continuation methods
• Bézout number calculations for multi-homogeneous polynomial systems
• Finding all isolated zeros of polynomial systems in \(\mathbb{C}^n\) via stable mixed volumes
• Why you cannot even hope to use Gröbner bases in public key cryptography: An open letter to a scientist who failed and a challenge to those who have not yet failed
• Minimizing multi-homogeneous Bézout numbers by a local search method
• Finding all isolated solutions to polynomial systems using HOMPACK
• Algorithm 795

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