A New Family Of Evd Tracking Algorithms Using Givens Rotations

In this work, we derive new algorithms for tracking the eigenvalue decomposition (EVD) of a time-varying data covariance matrix. These algorithms have parallel structures, low operation counts and good convergence behavior. Their main feature is the use of Givens rotations to update the eigenvector estimates. As a result, orthonormality of the latter can be maintained at all time, which is critical in the application of certain signal-subspace methods. The comparative performance of the new algorithms is illustrated by means of computer experiments. 1. INTRODUCTION In a recent paper [1], new EVD tracking algorithms were developed using a first-order perturbation approach. These algorithms exhibit attractive computational and convergence properties, but they suffer from a limitation common to many EVD tracking algorithms, namely: they do not produce perfectly orthonormal eigenvectors. In some applications, this is not important; in others, further orthonormalization of the eigenvectors..