Real Analysis Exchange
- Real Anal. Exchange
- Volume 42, Number 1 (2017), 149-166.
Quantization for Uniform Distributions on Equilateral Triangles
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.
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]
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