Suboptimal model reduction VIA least-square approximation of time-response by its derivatives and integrals

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

“…Consequently, in model order reduction applications, at least two reduced order models provably stable [9] can be readily obtained according to the procedure described in [14] for any given value of q .…”

“…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).…”

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

“…The Gram matrix of repeated integral and derivative functions possesses interesting properties [14,15], that allow reduction of the computing cost of the inner products (5). Indeed integration by parts of (2) yields…”

“…In order to derive reduced-order models taking the form of rational functions of order r = 6, Gram matrices of size (r +1)× (r +1) are calculated. We used the method described in [14,15] to derived some reduced models corresponding to the values q =1 , 2, ..., r +1. W e retained the reduced model that minimizes the relative quadratic error defined by…”

Orthogonal decomposition of derivatives and antiderivatives for easy evaluation of extended Gram matrix

“…Since the pioneering work of Jain [1,2] the Gram matrix has proved to be one of the most reliable tools in the field of model reduction [3][4][5][6]; its ability to produce good pole positions has motivated a number of papers. Early work has been devoted to the Gram matrix of successive antiderivatives of a time response.…”