Sanguo Zhu

activity

20142025

most citedAsymptotic order of the quantization errors for self-affine measures on Bedford-McMullen carpets

8 citations · 19 across the 12 of their papers we have counts for

collaborators

12 papers

math.CA2025

Convergence order of the quantization error for self-affine measures on Lalley-Gatzouras carpets

Sanguo Zhu

Let $E$ be a Lalley-Gatzouras carpet determined by a set of contractive affine mappings ${f_{ij}}_{(i, j) \in G}$ . We study the asymptotics of quantization error for the self-affin…

math.FA2024★ 1 cited

Asymptotic order of the quantization error for a class of self-similar measures with overlaps

Sanguo Zhu

Let ${f_{i}}_{i = 1}^{N}$ be a set of equi-contractive similitudes on $R^{1}$ satisfying the finite-type condition. We study the asymptotic quantization error for self-similar m…

math.FA2022★ 1 cited

Asymptotics of the quantization errors for some Markov-type measures with complete overlaps

Sanguo Zhu

Let $G$ be a directed graph with vertices $1, 2, \dots, 2 N$ . Let $T = (T_{i, j})_{(i, j) \in G}$ be a family of contractive similitudes. For every $1\leq i\l…

math.PR2020★ 1 cited

On the optimal Voronoi partitions for Ahlfors-David measures with respect to the geometric mean error

Sanguo Zhu, Youming Zhou

Let $μ$ be an Ahlfors-David probability measure on $R^{q}$ with support $K$ . For every $n \geq 1$ , let $C_{n} (μ)$ denote the collection of all the $n$ -optimal sets for $μ$ with…

math.FA2019

On the asymptotic quantization error for the doubling measures on Moran sets

Sanguo Zhu

We study the quantization errors for the doubling probability measures $μ$ which are supported on a class of Moran sets $E \subset R^{q}$ . For each $n \geq 1$ , let $α_{n}$ be an…

math.MG2019★ 1 cited

Asymptotic order of the geometric mean error for self-affine measures on Bedford-McMullen carpets

Sanguo Zhu, Shu Zou

Let $E$ be a Bedford-McMullen carpet associated with a set of affine mappings ${f_{ij}}_{(i, j) \in G}$ and let $μ$ be the self-affine measure associated with $\{f_{ij}\}_{(i,j)\in…

math.FA2018

Asymptotic uniformity of the quantization error for Moran measures on $R^{1}$

Sanguo Zhu

Let $E$ be a Moran set on $R^{1}$ associated with a closed interval $J$ and two sequences $(n_{k})_{k = 1}^{\infty}$ and $(C_{k} = (c_{k, j})_{j = 1}^{n_{k}})_{k \geq 1}$ . Let $μ$ …

math.MG2017★ 2 cited

Asymptotic local uniformity of the quantization error for Ahlfors-David probability measures

Sanguo Zhu

Let $μ$ be an Ahlfors-David probability measure on $R^{q}$ , namely, there exist some constants $s_{0} > 0$ and $ε_{0}, C_{1}, C_{2} > 0$ such that \[ C_1ε^{s_0}\leqμ(B(x,ε))\leq C_2ε^{s_0…

math.MG2016★ 1 cited

Exact convergence order of the $L_{r}$ -quantization error for Markov-type measures

Sanguo Zhu, Youming Zhou, Yongjian Sheng

Let $E$ be a graph-directed set associated with a di-graph $G$ . Let $μ$ be a Markov-type measure on $E$ . Assuming a separation condition for $E$ , we determine the exact convergence…

math.MG2016★ 8 cited

Asymptotic order of the quantization errors for self-affine measures on Bedford-McMullen carpets

Sanguo Zhu

Let $E$ be a Bedford-McMullen carpet determined by a set of affine mappings $(f_{ij})_{(i, j) \in G}$ and $μ$ a self-affine measure on $E$ associated with a probability vector $(p_{i…

math.MG2014★ 4 cited

Convergence order of the geometric mean errors for Markov-type measures

Sanguo Zhu

We study the quantization problem with respect to the geometric mean error for Markov-type measures $μ$ on a class of fractal sets. Assuming the irreducibility of the corresponding…

math.DS2014

Asymptotics of the geometric mean error for in-homogeneous self-similar measures

Sanguo Zhu, Youming Zhou, Yongjian Sheng

Let $(f_{i})_{i = 1}^{N}$ be a family of contractive similitudes on $R^{q}$ satisfying the open set condition. Let $(p_{i})_{i = 0}^{N}$ be a probability vector with $p_{i} > 0$ for all $i=…

Convergence order of the quantization error for self-affine measures on Lalley-Gatzouras carpets

Asymptotic order of the quantization error for a class of self-similar measures with overlaps

Asymptotics of the quantization errors for some Markov-type measures with complete overlaps

On the optimal Voronoi partitions for Ahlfors-David measures with respect to the geometric mean error

On the asymptotic quantization error for the doubling measures on Moran sets

Asymptotic order of the geometric mean error for self-affine measures on Bedford-McMullen carpets

Asymptotic uniformity of the quantization error for Moran measures on R1

Asymptotic local uniformity of the quantization error for Ahlfors-David probability measures

Exact convergence order of the Lr​-quantization error for Markov-type measures

Asymptotic order of the quantization errors for self-affine measures on Bedford-McMullen carpets

Convergence order of the geometric mean errors for Markov-type measures

Asymptotics of the geometric mean error for in-homogeneous self-similar measures

Asymptotic uniformity of the quantization error for Moran measures on $R^{1}$

Exact convergence order of the $L_{r}$ -quantization error for Markov-type measures