112 citations · 425 across the 52 of their papers we have counts for
11 papers · 1 filter
Superfast solution of Toeplitz systems based on syzygy reduction
Houssam Khalil, Bernard Mourrain, Michelle Schatzman
We present a new superfast algorithm for solving Toeplitz systems. This algorithm is based on a relation between the solution of such problems and syzygies of polynomials or moving…
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…
The DMM bound: multivariate (aggregate) separation bounds
Ioannis Z. Emiris, Bernard Mourrain, Elias Tsigaridas
In this paper we derive aggregate separation bounds, named after Davenport-Mahler-Mignotte (\dmm), on the isolated roots of polynomial systems, specifically on the minimum distance…
The Hilbert scheme of points and its link with border basis
Mariemi Alonso, Jérome Brachat, Bernard Mourrain
In this paper, we give new explicit representations of the Hilbert scheme of points in $\PP^{r}$ as a projective subvariety of a Grassmanniann variety. This new explicit descri…
Continued Fraction Expansion of Real Roots of Polynomial Systems
Angelos Mantzaflaris, Bernard Mourrain, Elias P. P. Tsigaridas
We present a new algorithm for isolating the real roots of a system of multivariate polynomials, given in the monomial basis. It is inspired by existing subdivision methods in the…
Symmetric tensor decomposition
Jerome Brachat, Pierre Comon, Bernard Mourrain +1
We present an algorithm for decomposing a symmetric tensor, of dimension n and order d as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 fo…