
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Document Type
Article
Publication Date
10-17-2022
Abstract
Let {Sj:1≤j≤3} be a set of three contractive similarity mappings such that Sj(x)=rx+j−12(1−r) for all x∈R, and 1≤j≤3, where 0
Let {Sj:1≤j≤3}">{Sj:1≤j≤3}{Sj:1≤j≤3} be a set of three contractive similarity mappings such that Sj(x)=rx+j−12(1−r)">Sj(x)=rx+j−12(1−r)Sj(x)=rx+j−12(1−r) for all x∈R">x∈Rx∈R, and 1≤j≤3">1≤j≤31≤j≤3, where 0Phas support the Cantor set generated by the similarity mappings Sj">SjSj for 1≤j≤3">1≤j≤31≤j≤3. Let r0=0.1622776602">r0=0.1622776602r0=0.1622776602, and r1=0.2317626315">r1=0.2317626315r1=0.2317626315 (which are ten digit rational approximations of two real numbers). In this paper, for 00n-means and the nth quantization errors for the triadic uniform Cantor distribution P for all positive integers n≥2">n≥2n≥2. Previously, Roychowdhury gave an exact formula to determine the optimal sets of n-means and the nth quantization errors for the standard triadic Cantor distribution, i.e., when r=15">r=15r=15. In this paper, we further show that r=r0">r=r0r=r0 is the greatest lower bound, and r=r1">r=r1r=r1 is the least upper bound of the range of r-values to which Roychowdhury formula extends. In addition, we show that for 00
Recommended Citation
Roychowdhury, Mrinal Kanti. "Optimal Quantization for Some Triadic Uniform Cantor Distributions with Exact Bounds." Qualitative theory of dynamical systems 21, no. 4 (2022): 149. https://doi.org/10.1007/s12346-022-00678-8
Publication Title
Qualitative Theory of Dynamical Systems
DOI
10.1007/s12346-022-00678-8
Comments
Original published version available at https://doi.org/10.1007/s12346-022-00678-8
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