Optimal quantization for a probability measure on a nonuniform stretched Sierpiński triangle

Abstract

Quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with support containing a finite number of elements. In this paper, we have considered a Borel probability measure $P$ on ${\mathbb{R}}^2$, which has support a nonuniform stretched Sierpiński triangle generated by a set of three contractive similarity mappings on ${\mathbb{R}}^2$. For this probability measure, we investigate the optimal sets of $n$-means and the $n$th quantization errors for all positive integers $n$.

arXiv admin note: text overlap with arXiv:1605.02281