School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Quantization for Uniform Distributions on Equilateral Triangles

Document Type

Article

Publication Date

3-27-2017

Abstract

We approximate the uniform measure on an equilateral triangle by a measure supported 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 the uniform distributions on general sets with piecewise smooth boundaries.

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Copyright © 2017 Michigan State University Press

Original published version available at https://projecteuclid.org/journals/real-analysis-exchange/volume-42/issue-1/Quantization-for-Uniform-Distributions-on-Equilateral-Triangles/rae/1490580015.full

Publication Title

Real Analysis Exchange

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