QUANTIZATION FOR UNIFORM DISTRIBUTIONS ON EQUILATERAL TRIANGLES

Carl P. Dettmann; Mrinal Kanti Roychowdhury

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QUANTIZATION FOR UNIFORM DISTRIBUTIONS ON EQUILATERAL TRIANGLES

机译：等边三角形均匀分布的量化

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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 ≤ 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 the uniform distributions on general sets with piecewise smooth boundaries.

机译：我们用n点支持的测度近似等边三角形上的均匀测度。我们找到n≤4的最佳点集（n均值）和相应的近似值（量化）误差，给出n≤21的数值优化结果，并确定n→∞的量化误差。由于等边三角形与三角形晶格的连接，因此具有特别有效的量化。我们的方法可以应用于具有分段光滑边界的一般集合上的均匀分布。

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来源
《Real analysis exchange》 |2017年第1期|149-166|共18页
作者
Carl P. Dettmann; Mrinal Kanti Roychowdhury;
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作者单位

University of Bristol, School of Mathematics, University Walk, Bristol BS8 1TW, UK;

School of Mathematical and Statistical Sciences, University of Texas Rio Grande Valley, 1201 West University Drive, Edinburg, TX 78539-2999, USA;

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8. NOMOGRAMS FOR OBTAINING THE ARRIVAL ANGLE AND BEARING OF RADIO WAVES FROM MEASUREMENTS OF PHASE DIFFERENCE BETWEEN THREE STATIONS ARRANGED IN AN EQUILATERAL TRIANGLE [R] . 1963

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QUANTIZATION FOR UNIFORM DISTRIBUTIONS ON EQUILATERAL TRIANGLES

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