34 citations · 59 across the 7 of their papers we have counts for
5 papers · 1 filter
Deflation and Certified Isolation of Singular Zeros of Polynomial Systems
Angelos Mantzaflaris, Bernard Mourrain
We develop a new symbolic-numeric algorithm for the certification of singular isolated points, using their associated local ring structure and certified numerical computations. An…
A Sparse Flat Extension Theorem for Moment Matrices
Monique Laurent, Bernard Mourrain
In this note we prove a generalization of the flat extension theorem of Curto and Fialkow for truncated moment matrices. It applies to moment matrices indexed by an arbitrary set o…
Moment matrices, trace matrices and the radical of ideals
Itnuit Janovitz-Freireich, Agnes Szanto, Bernard Mourrain +1
Let be a system of polynomials generating a zero-dimensional ideal $\I$, where is an arbitrary algebraically closed field. As…
Stable normal forms for polynomial system solving
Bernard Mourrain, Philippe Trébuchet
This paper describes and analyzes a method for computing border bases of a zero-dimensional ideal . The criterion used in the computation involves specific commutation polynomia…
Explicit factors of some iterated resultants and discriminants
Laurent Busé, Bernard Mourrain
In this paper, the result of applying iterative univariate resultant constructions to multivariate polynomials is analyzed. We consider the input polynomials as generic polynomials…