Least-change secant update methods for undetermined systems
SIAM Journal on Numerical Analysis
Improved error bounds for underdetermined system solvers
SIAM Journal on Matrix Analysis and Applications
Computing rank-revealing QR factorizations of dense matrices
ACM Transactions on Mathematical Software (TOMS)
Algorithm 782: codes for rank-revealing QR factorizations of dense matrices
ACM Transactions on Mathematical Software (TOMS)
A New Criterion for Normal Form Algorithms
AAECC-13 Proceedings of the 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
The Construction of Multivariate Polynomials with Preassigned Zeros
EUROCAM '82 Proceedings of the European Computer Algebra Conference on Computer Algebra
Numerical Polynomial Algebra
"Approximate Commutative Algebra": an ill-chosen name for an important discipline
ACM Communications in Computer Algebra
Stable border bases for ideals of points
Journal of Symbolic Computation
Computational Commutative Algebra 1
Computational Commutative Algebra 1
Approximate computation of zero-dimensional polynomial ideals
Journal of Symbolic Computation
| Hi-index | 5.23 |
Given a finite set X of points and a tolerance @e representing the maximum error on the coordinates of each point, we address the problem of computing a simple polynomial f whose zero-locus Z(f) ''almost'' contains the points of X. We propose a symbolic-numerical method that, starting from the knowledge of X and @e, determines a polynomial f whose degree is strictly bounded by the minimal degree of the elements of the vanishing ideal of X. Then, in Theorem 4.3, we state the sufficient conditions for proving that Z(f) lies close to each point of X by less than @e. The validity of the proposed method relies on a combination of classical results of Computer Algebra and Numerical Analysis; its effectiveness is illustrated with a number of examples.