Simple varieties for limited precision points

DOI10.1016/j.tcs.2012.10.024zbMath1291.65081arXiv1008.0274OpenAlexW1963775544MaRDI QIDQ385012

Claudia Fassino, Maria-Laura Torrente

Publication date: 29 November 2013

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

Full work available at URL: https://arxiv.org/abs/1008.0274

zbMATH Keywords

affine varietyempirical pointssymbolic-numerical algorithms

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Real polynomials: location of zeros (26C10) Numerical approximation and computational geometry (primarily algorithms) (65D99) Solving polynomial systems; resultants (13P15)

Related Items (4)

Noise-tolerant algebraic method for reconstruction of nonlinear dynamical systems ⋮ Verification of a low-degree polynomial vanishing at empirical points ⋮ Verified error bounds for eigenvalues of geometric multiplicity \(q\) and corresponding invariant subspaces ⋮ Almost vanishing polynomials and an application to the Hough transform

Uses Software

• CoCoA
• RRQR
• toms/782

Cites Work

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• Approximate computation of zero-dimensional polynomial ideals
• Approximate commutative algebra
• Stable border bases for ideals of points
• Almost vanishing polynomials for sets of limited precision points
• Approximate varieties, approximate ideals and dimension reduction
• Thinning out redundant empirical data
• Subideal border bases
• Least-Change Secant Update Methods for Underdetermined Systems
• Rank-Revealing QR Factorizations and the Singular Value Decomposition
• Improved Error Bounds for Underdetermined System Solvers
• Computing rank-revealing QR factorizations of dense matrices
• Algorithm 782
• Numerical Polynomial Algebra

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