STABILIZATION OF SPECTRAL METHODS FOR THE ANALYSIS OF SINGULAR SYSTEMS USING PIECEWISE-CONSTANT BASIS FUNCTIONS

The analysis of initial value problems associated with singular linear dynamic systems using spectral methods is discussed. These methods, t hough extensively studied in the literature, can be very sensitive to numerical errors and to the presence of noisy input data. Moreover, us ing piecewise constant functions, like Walsh or Block-Pulse, spectral methods have been shown to be unstable with respect to incorrect initi al conditions. In this paper regularization techniques are used to red uce arbitrarily the sensitivity of the spectral methods, and at the sa me time to stabilize them. Although the regularized spectral methods m aintain the structure of the original algorithm, they can also be rewr itten in recursive form, leading to the definition of a class of discr ete time filters. Finally, some applicative numerical examples are dis cussed in order to show the effectiveness of the proposed algorithms.