112 citations · 425 across the 52 of their papers we have counts for
4 papers · 2 filters
Flat extensions in *-algebras
Bernard Mourrain, Konrad Schmüdgen
The main result of the paper is a flat extension theorem for positive linear functionals on *-algebras. The theorem is applied to truncated moment problems on cylinder sets, on mat…
Toric Border Bases
Bernard Mourrain, Philippe Trebuchet
We extend the theory and the algorithms of Border Bases to systems of Laurent polynomial equations, defining "toric" roots. Instead of introducing new variables and new relations t…
Border Basis relaxation for polynomial optimization
Marta Abril Bucero, Bernard Mourrain
A relaxation method based on border basis reduction which improves the efficiency of Lasserre's approach is proposed to compute the optimum of a polynomial function on a basic clos…
Bounds on the dimension of trivariate spline spaces: A homological approach
Bernard Mourrain, Nelly Villamizar
We consider the vector space of globally differentiable piecewise polynomial functions defined on a three-dimensional polyhedral domain partitioned into tetrahedra. We prove new lo…