3 citations · 11 across the 13 of their papers we have counts for
13 papers
Universal minima of potentials of certain spherical designs contained in the fewest parallel hyperplanes
Sergiy Borodachov
We find the set of all universal minimum points of the potential of the -point sharp code on and (more generally) of the demihypercube on , , as well as of…
Pointwise optimal multivariate spline method for recovery of twice differentiable functions on a simplex
Sergiy Borodachov
We obtain the spline recovery method on a -dimensional simplex that uses as information values and gradients of a function at the vertices of and is optimal for reco…
Absolute Minima of Potentials of a Certain Class of Spherical Designs
Sergiy Borodachov
We use linear programming techniques to find points of absolute minimum over the unit sphere in of the total potential of a point configuration $ω_N\subse…
Optimal Antipodal Configuration of Points on a Sphere in for Covering
Sergiy Borodachov
We show that among antipodal -point configurations on the sphere in , the set of vertices of a regular cross-polytope inscribed in uniquely sol…
Absolute Minima of Potentials of Certain Regular Spherical Configurations
Sergiy Borodachov
We use methods of approximation theory to find the absolute minima on the sphere of the potential of spherical -designs with a non-trivial index that are contained in…
Min-Max Polarization for Certain Classes of Sharp Configurations on the Sphere
Sergiy Borodachov
We consider the problem of finding an -point configuration on the sphere $S^d\subset \RR^{d+1}$ with the smallest absolute maximum value over of its total potential. The p…