Quantization for uniform distributions on equilateral triangles

Carl Dettmann, Mrinal Roychowdhury

Research output: Contribution to journalArticle (Academic Journal)peer-review

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We approximate the uniform measure on an equilateral triangle by a measure sup-
ported on n points. We find the optimal sets of points (n-means) and corresponding approximation (quantization) error for n≤4, give numerical optimization results for n≤21, and a bound on the quantization error for n→∞. The equilateral triangle has particularly efficient quantizations due to its connection with the triangular lattice. Our methods can be applied to uniform distributions on general sets with piecewise smooth boundaries.
Original languageEnglish
JournalReal Analysis Exchange
Issue number1
Early online date27 Mar 2017
Publication statusPublished - 2017


  • Uniform distributions
  • optimal sets
  • quantization error


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