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arXiv · 1909.00981

Upper bounds for energies of spherical codes of given cardinality and separation

Peter Boyvalenkov·Peter Dragnev·Douglas Hardin·Edward Saff·Maya Stoyanova
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Abstract

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 interpolation we construct polynomials to derive corresponding bounds. These bounds are universal in the sense that they are valid for all absolutely monotone potential functions and the required interpolation nodes do not depend on the potentials.

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Peter Boyvalenkov, Peter Dragnev, Douglas Hardin, Edward Saff, Maya Stoyanova. 2019-09-03. Upper bounds for energies of spherical codes of given cardinality and separation. https://arxiv.org/abs/1909.00981

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