Open Access
2017 Quantization for Uniform Distributions on Equilateral Triangles
Carl P. Dettmann, Mrinal Kanti Roychowdhury
Real Anal. Exchange 42(1): 149-166 (2017).


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 $n\leq4$, give numerical optimization results for $n\leq 21$, and a bound on the quantization error for $n\to\infty$. 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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Carl P. Dettmann. Mrinal Kanti Roychowdhury. "Quantization for Uniform Distributions on Equilateral Triangles." Real Anal. Exchange 42 (1) 149 - 166, 2017.


Published: 2017
First available in Project Euclid: 27 March 2017

zbMATH: 06848944
MathSciNet: MR3702559

Primary: 60Exx , 94A34
Secondary: 62Exx

Keywords: optimal sets , quantization error , uniform distributions

Rights: Copyright © 2017 Michigan State University Press

Vol.42 • No. 1 • 2017
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