Discrepancy, separation and Riesz energy of finite point sets on the unit sphere

Paul Leopardi*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    13 Citations (Scopus)

    Abstract

    For d ≥ 2 we consider asymptotically equidistributed sequences of Sd codes, with an upper bound δ on spherical cap discrepancy, and a lower bound Δ on separation. For such sequences, if 0 < s < d, then the difference between the normalized Riesz s energy of each code, and the normalized s-energy double integral on the sphere is bounded above by O(δ1-s/dΔ-sN-s/d where N is the number of code points. For well separated sequences of spherical codes, this bound becomes δ1-s/d We apply these bounds to minimum energy sequences, sequences of well separated spherical designs, sequences of extremal fundamental systems, and sequences of equal area points.

    Original languageEnglish
    Pages (from-to)27-43
    Number of pages17
    JournalAdvances in Computational Mathematics
    Volume39
    Issue number1
    DOIs
    Publication statusPublished - Jul 2013

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