Real Analysis Exchange

Quantization for Uniform Distributions on Equilateral Triangles

Carl P. Dettmann and Mrinal Kanti Roychowdhury

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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 $n\leq4$, 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

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

Dates
First available in Project Euclid: 27 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.rae/1490580015

Mathematical Reviews number (MathSciNet)
MR3702559

Zentralblatt MATH identifier
06848944

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

Keywords
uniform distributions optimal sets quantization error

Citation

Dettmann, Carl P.; Roychowdhury, Mrinal Kanti. Quantization for Uniform Distributions on Equilateral Triangles. Real Anal. Exchange 42 (2017), no. 1, 149--166. https://projecteuclid.org/euclid.rae/1490580015


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