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Asymptotical Orthonormalization of Subspace Matrices Without Square Root

Abstract

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 subspacematrices. 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 squareroot. This method is among a class of normalization methods that allow a simple adaptive implementation of the power method for subspace tracking.

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