5 citations · 8 across the 8 of their papers we have counts for
6 papers · 1 filter
Bounds on energy and potentials of discrete measures on the sphere
S. Borodachov, P. Boyvalenkov, P. Dragnev +3
We establish upper and lower universal bounds for potentials of weighted designs on the sphere that depend only on quadrature nodes and weights derived from the…
Bounds on Discrete Potentials of Spherical (k,k)-Designs
S. Borodachov, P. Boyvalenkov, P. Dragnev. D. Hardin. E. Saff +1
We derive universal lower and upper bounds for max-min and min-max problems (also known as polarization) for the potential of spherical -designs and provide certain examples…
Upper bounds for energies of spherical codes of given cardinality and separation
Peter Boyvalenkov, Peter Dragnev, Douglas Hardin +2
We introduce a linear programming framework for obtaining upper bounds for the potential energy of spherical codes of fixed cardinality and minimum distance. Using Hermite interpol…
Energy Bounds for Codes in Polynomial Metric Spaces
Peter Boyvalenkov, Peter Dragnev, Douglas Hardin +2
In this article we present a unified treatment for obtaining bounds on the potential energy of codes in the general context of polynomial metric spaces (PM-spaces). The lower bound…
On spherical codes with inner products in a prescribed interval
P. G. Boyvalenkov, P. D. Dragnev, D. P. Hardin +2
We develop a framework for obtaining linear programming bounds for spherical codes whose inner products belong to a prescribed subinterval of . An intricate rela…
Universal lower bounds for potential energy of spherical codes
P. G. Boyvalenkov, P. D. Dragnev, D. P. Hardin +2
We derive and investigate lower bounds for the potential energy of finite spherical point sets (spherical codes). Our bounds are optimal in the following sense -- they cannot be im…