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Asymptotical orthonormalization of subspace matrices without square root

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1 Author(s)
Hua, Y. ; Dept. of Electr. Eng., California Univ., Riverside, CA, USA

Subspace computation is fundamental for many signal processing applications. A well-known tool for computing the principal subspace of a data matrix is the power method. During the iterations of the power method, a proper normalization is essential to avoid numerical overflow or underflow. Normalization is also needed to achieve desirable properties such as orthonormalized subspace matrices. A number of normalization techniques for the power method is reviewed, which include the conventional as well as nonconventional ones. In particular, a new method of normalization is introduced to achieve asymptotical orthonormalization of subspace matrices without the use of square root. This method is among a class of normalization methods that allow a simple adaptive implementation of the power method for subspace tracking.

Published in:

Signal Processing Magazine, IEEE  (Volume:21 ,  Issue: 4 )