DocumentCode
939152
Title
Relationship between the Karhunen- Loéve transform and the Courant - Fischer theorem (Corresp.)
Author
Delsarte, Philippe ; Kamp, Yves
Volume
30
Issue
4
fYear
1984
fDate
7/1/1984 12:00:00 AM
Firstpage
662
Lastpage
664
Abstract
It is shown that the Karhunen-Loève transform problem can be formulated as a matrix approximation problem with Hilbert-Schmidt error norm. On the other hand, the Courant-Fischer minimax theorem provides a characterization for the best matrix approximation when the spectral norm is used. It appears that the optimality conditions of the Karhunen-Loève problem lead to the selection of a particular solution among the set of solutions to the Courant-Fischer problem.
Keywords
Karhunen-Loeve transforms; Matrices; Minimax approximation; Channel capacity; Covariance matrix; Data compression; Discrete transforms; Eigenvalues and eigenfunctions; Hilbert space; Karhunen-Loeve transforms; Minimax techniques; Quantization; Vectors;
fLanguage
English
Journal_Title
Information Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9448
Type
jour
DOI
10.1109/TIT.1984.1056938
Filename
1056938
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