The Geometry of Multivariate Polynomial Division and Elimination

DOI10.1137/120863782zbMath1269.65026OpenAlexW2044376508MaRDI QIDQ5300548

Kim Batselier, Philippe Dreesen, Bart De Moor

Publication date: 27 June 2013

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/c0cc81c6ca1b63eeadeeaf32b16b1e3c2d95ef63

zbMATH Keywords

Gröbner basisnumerical examplessparse matricesQR decompositionalgebraic geometryoblique projectionCS decompositionprincipal anglesmultivariate polynomial divisionmultivariate polynomial elimination

Mathematics Subject Classification ID

Related Items (9)

Random sampling in computational algebra: Helly numbers and violator spaces ⋮ Inverse multivariate polynomial root-finding: numerical implementations of the affine and projective Buchberger-Möller algorithm ⋮ A fast recursive orthogonalization scheme for the Macaulay matrix ⋮ Recursive Algorithms to Update a Numerical Basis Matrix of the Null Space of the Block Row, (Banded) Block Toeplitz, and Block Macaulay Matrix ⋮ On the null spaces of the Macaulay matrix ⋮ Computing the state difference equations for discrete overdetermined linear \(m \operatorname{D}\) systems ⋮ Control of MIMO nonlinear systems: a data-driven model inversion approach ⋮ A linear algebra method to decompose forms whose length is lower than the number of variables into weighted sum of squares ⋮ Two complementary block Macaulay matrix algorithms to solve multiparameter eigenvalue problems

Uses Software

• SuiteSparseQR
• SuitSparseQR
• na20

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