Families of orthonormalization algorithms

Mohammed A. Hasan

doi:10.1109/IJCNN.2009.5178956

Families of orthonormalization algorithms

Mohammed A. Hasan

Electrical Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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.

Original language	English (US)
Title of host publication	2009 International Joint Conference on Neural Networks, IJCNN 2009
Pages	1122-1127
Number of pages	6
DOIs	https://doi.org/10.1109/IJCNN.2009.5178956
State	Published - 2009
Event	2009 International Joint Conference on Neural Networks, IJCNN 2009 - Atlanta, GA, United States Duration: Jun 14 2009 → Jun 19 2009

Publication series

Name	Proceedings of the International Joint Conference on Neural Networks

Other

Other	2009 International Joint Conference on Neural Networks, IJCNN 2009
Country/Territory	United States
City	Atlanta, GA
Period	6/14/09 → 6/19/09

Keywords

Global convergence
Global stability
Gram-schmidt process
Lyapunov stability
Orthonormalization
Unconstrained optimization

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Hasan, MA 2009, Families of orthonormalization algorithms. in 2009 International Joint Conference on Neural Networks, IJCNN 2009., 5178956, Proceedings of the International Joint Conference on Neural Networks, pp. 1122-1127, 2009 International Joint Conference on Neural Networks, IJCNN 2009, Atlanta, GA, United States, 6/14/09. https://doi.org/10.1109/IJCNN.2009.5178956

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AB - 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.

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KW - Global stability

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KW - Lyapunov stability

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KW - Unconstrained optimization

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ER -

Families of orthonormalization algorithms

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