Gram matrix of a Laguerre model: application to model reduction of irrational transfer function

Abstract

To cite this version:Noël Tanguy

Efficient Gram-matrix computation for irrational resonant systems using Kautz models

“…Using the properties of the Gram matrix given in [11], an efficient algorithm for its computation is summarized in the appendix. …”

“…A set of reduced order 3 models, guaranteed to be stable, can readily be derived using the method described in [14] is clearly more precise benefiting from a very accurate computation of the Gram matrix with a relatively small number of Kautz coefficients. Due to the highly resonant nature of the system, achieving such accuracy via a Laguerre decomposition as described in [11] would require a much greater number of coefficients (several hundred for a well chosen Laguerre parameter). For the sake of comparison we specify that the use of 10 Laguerre coefficients would in this case lead to a relatively bad model with a respective quadratic error The second example we present is the band-pass circuit in Fig.4.…”

“…first proposed by Johnson [4]. The impulse response of the original system, the reduced order 4 model given above, and the best order 4 model computed by the use of Laguerre functions instead of Kautz [11] are shown in Fig.5. The difference in accuracy is visible, especially in Fig.6., where the variation of the squared error is plotted.…”

Laguerre-gram reduced order modeling applied to VLSI circuit interconnects

“…12 11 (6) The first advantage of such a representation is that this matrix is persymmetrical, thus we obtain a complete description of the circuit with only two matrix terms. But what is even more important is that it greatly facilitates future work on passivity enforcement.…”

“…Tools have therefore been developed to enable the approximation of full interconnect models by simpler, more versatile ones. The method we propose in this paper benefits from recent research on Laguerre representations [2], [6].…”