A geometrical approach to finding multivariate approximate LCMs and GCDs

DOI10.1016/j.laa.2012.12.043zbMath1337.65033OpenAlexW2039073905MaRDI QIDQ1947122

Bart De Moor, Philippe Dreesen, Kim Batselier

Publication date: 12 April 2013

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2012.12.043

zbMATH Keywords

singular valuesmultivariate polynomialsArnoldi iterationapproximate GCDprincipal anglesapproximate LCM

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical solutions to overdetermined systems, pseudoinverses (65F20) Inequalities involving eigenvalues and eigenvectors (15A42) Numerical computation of matrix norms, conditioning, scaling (65F35)

Related Items (7)

Affine equivalences of trigonometric curves ⋮ Approximate least common multiple of several polynomials using the ERES division algorithm ⋮ A fast recursive orthogonalization scheme for the Macaulay matrix ⋮ On the null spaces of the Macaulay matrix ⋮ SLRA Interpolation for Approximate GCD of Several Multivariate Polynomials ⋮ Approximate polynomial GCD by approximate syzygies ⋮ Exact and approximate similarities of non-necessarily rational planar, parametrized curves, using centers of gravity and inertia tensors

Uses Software

• SuiteSparseQR

Cites Work

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• The calculation of the degree of an approximate greatest common divisor of two polynomials
• A Gershgorin-type lower bound for the smallest singular value
• Products of polynomials in many variables
• Quasi-gcd computations
• Approximate GCD and its application to ill-conditioned algebraic equations
• On approximate GCDs of univariate polynomials
• Certified approximate univariate GCDs
• Common factor detection and estimation
• Approximate factorization of multivariate polynomials using singular value decomposition
• An elementary proof of Barnett's theorem about the greatest common divisor of several univariate polynomials
• Computing greatest common divisors and squarefree decompositions through matrix methods: the parametric and approximate cases
• Algorithm 915, SuiteSparseQR
• The approximate GCD of inexact polynomials
• Deflation Techniques for an Implicitly Restarted Arnoldi Iteration
• Numerical Methods for Computing Angles Between Linear Subspaces
• <tex>$QR$</tex>Factoring to Compute the GCD of Univariate Approximate Polynomials

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