Families of orthonormalization algorithms

Authors:
Mohammed A. Hasan
Affiliations:
Department of Electrical & Computer Engineering, University of Minnesota, Duluth, MN
Venue:
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Year:
2009

Citing 4
Cited 0

Original Contribution: Principal components, minor components, and linear neural networks

Neural Networks
Jacobi--Davidson Style QR and QZ Algorithms for the Reduction of Matrix Pencils

SIAM Journal on Scientific Computing
The Geometry of Algorithms with Orthogonality Constraints

SIAM Journal on Matrix Analysis and Applications
Square-root free orthogonalization algorithms

ICASSP '09 Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing

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Abstract

In the development of adaptive systems in control theory and signal processing, it frequently occurs that the problem of orthonormalization must be addressed. This paper explored the underlying mathematical framework of developing orthonormalization methods that are free of computing matrix square roots. These algorithms are easily modified so that minor and principal component analysis methods are developed. The proposed methods have several important features: 1) higher order convergence can be achieved by choosing a specific stepsize, 2) the methods can be used to compute square root of positive definite matrices.