DocumentCode
1162640
Title
On convergence of Lloyd´s method I
Author
Wu, Xiaolin
Author_Institution
Dept. of Comput. Sci., Univ. of Western Ontario, London, Ont., Canada
Volume
38
Issue
1
fYear
1992
fDate
1/1/1992 12:00:00 AM
Firstpage
171
Lastpage
174
Abstract
Although Lloyd´s method I for optimal quantization was proposed more than thirty years ago and has been frequently referred to in the literature, its convergence has so far not been shown. This correspondence proves that Lloyd´s method I converges for a large class of error measures, if the density function is continuous, positive, and defined on a finite interval. The proof is done by modeling the behavior of a continuous optimization algorithm by a finite state machine
Keywords
convergence of numerical methods; finite automata; information theory; Lloyd´s method I; continuous optimization algorithm; convergence; error measures; finite state machine; optimal quantization; Automata; Books; Convergence; Density functional theory; Iterative algorithms; Partitioning algorithms; Quantization; Spectrogram; Strips; Strontium;
fLanguage
English
Journal_Title
Information Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9448
Type
jour
DOI
10.1109/18.108266
Filename
108266
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