The Canonical Decomposition of $\mathcal{C}^n_d$ and Numerical Gröbner and Border Bases

DOI10.1137/130927176zbMath1327.13103OpenAlexW1995228508MaRDI QIDQ5246479

Bart De Moor, Kim Batselier, Philippe Dreesen

Publication date: 21 April 2015

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

Full work available at URL: https://doi.org/10.1137/130927176

zbMATH Keywords

Gröbner basissingular value decompositionmultivariate polynomialsborder basisMacaulay matrixprincipal angles

Mathematics Subject Classification ID

Factorization of matrices (15A23) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Eigenvalues, singular values, and eigenvectors (15A18) Vector spaces, linear dependence, rank, lineability (15A03) Toeplitz, Cauchy, and related matrices (15B05) Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) (13P25)

Related Items (7)

Inverse multivariate polynomial root-finding: numerical implementations of the affine and projective Buchberger-Möller algorithm ⋮ A fast recursive orthogonalization scheme for the Macaulay matrix ⋮ On the null spaces of the Macaulay matrix ⋮ Multidimensional realisation theory and polynomial system solving ⋮ Numerical computation of H-bases ⋮ Computing H-bases via minimal bases for syzygy modules ⋮ A linear algebra method to decompose forms whose length is lower than the number of variables into weighted sum of squares

Uses Software

• Matlab
• Octave
• PHCpack

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