Abstract
We approximate the uniform measure on an equilateral triangle by a measure sup-
ported 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 uniform distributions on general sets with piecewise smooth boundaries.
ported 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 uniform distributions on general sets with piecewise smooth boundaries.
| Original language | English |
|---|---|
| Journal | Real Analysis Exchange |
| Volume | 42 |
| Issue number | 1 |
| Early online date | 27 Mar 2017 |
| Publication status | Published - 2017 |
Keywords
- Uniform distributions
- optimal sets
- quantization error