Universal optimal configurations for the $p$-frame potentials

@article{Chen2020UniversalOC,
  title={Universal optimal configurations for the \$p\$-frame potentials},
  author={Xuemei Chen and Victor Gonzales and E. Goodman and Shujie Kang and K. Okoudjou},
  journal={Adv. Comput. Math.},
  year={2020},
  volume={46},
  pages={4}
}
Given $d, N\geq 2$ and $p\in (0, \infty]$ we consider a family of functionals, the $p$-frame potentials FP$_{p, N, d}$, defined on the set of all collections of $N$ unit-norm vectors in $\mathbb R^d$. For the special case $p=2$ and $p=\infty$, both the minima and the minimizers of these potentials have been thoroughly investigated. In this paper, we investigate the minimizers of the functionals FP$_{p, N, d}$, by first establishing some general properties of their minima. Thereafter, we focus… Expand
8 Citations
The minimizers of the $p$-frame potential
  • 2
  • Highly Influenced
  • PDF
Repeated Minimizers of p-Frame Energies
  • 1
  • Highly Influenced
A variational characterisation of projective spherical designs over the quaternions
  • 1
  • PDF
FA ] 3 0 Ju l 2 01 9 THE MINIMIZERS OF THE p-FRAME POTENTIAL
  • Highly Influenced
On the Search for Tight Frames of Low Coherence
  • PDF
On a frame energy problem.
  • PDF
Moments of isotropic measures and optimal projective codes
  • 6
  • PDF
Large signed subset sums
  • PDF

References

SHOWING 1-10 OF 29 REFERENCES
The minimizers of the $p$-frame potential
  • 2
  • PDF
Minimizing the $p$-frame potential
  • 5
  • Highly Influential
  • PDF
Finite two-distance tight frames
  • 31
  • PDF
Universally optimal distribution of points on spheres
  • 280
  • Highly Influential
  • PDF
Nearly orthogonal vectors and small antipodal spherical codes
  • 12
  • PDF
Frame Potentials and the Geometry of Frames
  • 16
  • PDF
GRASSMANNIAN FRAMES WITH APPLICATIONS TO CODING AND COMMUNICATION
  • 856
  • PDF
Minimization of the probabilistic p-frame potential
  • 43
  • PDF
Geometric Properties of Grassmannian Frames for and
  • 31
...
1
2
3
...