Title :
Relationship between the Karhunen- Loéve transform and the Courant - Fischer theorem (Corresp.)
Author :
Delsarte, Philippe ; Kamp, Yves
fDate :
7/1/1984 12:00:00 AM
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;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.1984.1056938
