CAUSAL EIGENVECTOR FUNCTION APPROXIMATIONS AND THE PROBLEM OF SCALING - AN ALGORITHM

Eigenvector scaling implies the existence of degrees of freedom in the power series approximations of the eigenvector and dual eigenvector functions of the discrete-time transfer-function matrix. An earlier paper gave consideration to the anti-clockwise winding associated with anti-causality and proposed an algorithm which scaled eigenvectors with a view to reducing their anti-causal component. The present paper proposes a different algorithm which, although still formulated in the frequency domain, places a direct penalty on the time-domain anti-causal component of the eigenvector sequences and avoids some of the aliasing difficulties that could arise in connection with the earlier algorithm. The new algorithm also provides the systematic means of reducing the length of the causal component of the associated vector sequences and results in better eigenvector approximations, as illustrated by two numerical examples.