Real Analysis Exchange

Quantization for Uniform Distributions on Equilateral Triangles

Carl P. Dettmann and Mrinal Kanti Roychowdhury

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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.

Article information

Real Anal. Exchange, Volume 42, Number 1 (2017), 149-166.

First available in Project Euclid: 27 March 2017

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60Exx: Distribution theory [See also 62Exx, 62Hxx] 94A34: Rate-distortion theory
Secondary: 62Exx: Distribution theory [See also 60Exx]

uniform distributions optimal sets quantization error


Dettmann, Carl P.; Roychowdhury, Mrinal Kanti. Quantization for Uniform Distributions on Equilateral Triangles. Real Anal. Exchange 42 (2017), no. 1, 149--166.

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