Families of orthonormalization algorithms

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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 languageEnglish (US)
Title of host publication2009 International Joint Conference on Neural Networks, IJCNN 2009
Number of pages6
StatePublished - 2009
Event2009 International Joint Conference on Neural Networks, IJCNN 2009 - Atlanta, GA, United States
Duration: Jun 14 2009Jun 19 2009

Publication series

NameProceedings of the International Joint Conference on Neural Networks


Other2009 International Joint Conference on Neural Networks, IJCNN 2009
Country/TerritoryUnited States
CityAtlanta, GA


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


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