SINGULAR VALUE ANALYSIS OF PREDICTOR MATRICES

Predictor matrices arise in problems of science and engineering where one is interested in predicting future information from previous ones using linear models. The solution of such problems depends on an accurate estimate of a part of the spectrum (the signal eigenvalues) of these matrices. In this paper, singular values of predictor matrices are analysed and formulae for their computation are derived. By applying a well-known eigenvalue–singular value inequality to our results, we deduce lower and upper bounds on the modulus of signal eigenvalues. These bounds depend on the dimension of the problem and allow us to show that the magnitude of signal eigenvalues is relatively insensitive to small perturbations in the data, provided the signal is slightly damped and the dimension of the problem is large enough. The theory is illustrated by numerical examples including the analysis of a signal arising from experimental measurements.