Approximate polynomial GCD by approximate syzygies

DOI10.1007/s11786-019-00392-wzbMath1474.13053OpenAlexW2922789258WikidataQ128198355 ScholiaQ128198355MaRDI QIDQ2009224

Daniel A. Lichtblau

Publication date: 27 November 2019

Published in: Mathematics in Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11786-019-00392-w

zbMATH Keywords

linear programmingquadratic programmingsyzygiesapproximate polynomial GCDhybrid symbolic-numeric algorithmsnumeric Gröbner basis

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Polynomials, factorization in commutative rings (13P05) Approximation algorithms (68W25)

Related Items (1)

SLRA Interpolation for Approximate GCD of Several Multivariate Polynomials

Uses Software

• CoCoA
• CoCoALib
• Macaulay2
• Mathematica

Cites Work

• Approximate GCD and its application to ill-conditioned algebraic equations
• An algorithm for computing certified approximate GCD of \(n\) univariate polynomials
• Floating point Gröbner bases.
• Computation of approximate polynomial GCDs and an extension
• A geometrical approach to finding multivariate approximate LCMs and GCDs
• Approximate multivariate polynomial factorization based on zero-sum relations
• Approximate greatest common divisors of several polynomials with linearly constrained coefficients and singular polynomials
• Computing multivariate approximate GCD based on Barnett's theorem
• Approximate factorization of multivariate polynomials via differential equations
• Numerical Polynomial Algebra
• Applications of strong Grobner bases over Euclidean domains
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