Families of orthonormalization algorithms

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.