Reduced state-space models obtained by model order reduction methods must be accurate over the whole frequency range of interest and must also preserve passivity.In this paper, we propose multipoint reduction technique using reflective exploration for adaptively choosing the expansion points.The projection matrices obtained from the expansion points are merged to form the overall projection matrix.In order to obtain a more compact model the projection matrix is truncated based on its singular values.Finally, the reduced order model is obtained, while ensuring that the passivity of the reduced system is preserved during the reduction process.

A novel state-space realization for parametric macromodeling is proposed in this paper.A judicious choice of the state-space realization is required to account for the generally assumed smoothness of the state-space matrices with respect to the design parameters.This is used in combination with suitable interpolation schemes to interpolate a set of state-space matrices, and hence the poles and residues indirectly, in order to build accurate parametric macromodels.The key points are the choice of a proper pivot matrix and the solution of a Sylvester equation for pole placement.Pertinent numerical examples validate the proposed state-space realization for parametric macromodeling.

This paper describes a robust and accurate black-box macromodeling technique, in which the constitutive equations combine both closed-form delay operators and low-order rational coefficients. These models describe efficiently electrically long interconnect links. The algorithm is based on an iterative weighted least-squares process and can be interpreted as a generalization of the well-known Vector Fitting. The paper is focused, in particular, on the passivity enforcement of these models. We present two perturbation methods and we show how the accuracy of the models is well-preserved during the passivity enforcement process.

First, I would like to thank the author of "Comments on 'A Simple and Accurate Algorithm for Barycentric Rational Interpolation'" (hereafter referred to as "the comments") for their interest in my work [1]. The author of the comments points out a novel relationship between barycentric rational interpolation, the Welch-Berlekamp key equation and Grobner bases. This could turn out to be a very promising novel approach for fast barycentric interpolation, since as to this author's knowledge, the results about barycentric interpolation available in the literature (see references [13-17] in [1]) never mention the potential link with the Welch-Berlekamp key equation and/or Grobner bases. However, the results in [1] with respect to the null space of a certain Lowner matrix have not been invalidated by the comments. As a last remark, it should be noted that the null space of a matrix can be calculated by other means than the SVD, e.g. by the "cheaper" QR decomposition.

A very simple noniterative signal approximation scheme based on rational barycentric interpolation and the null-space of a Lowner matrix is presented. Numerical examples demonstrate the accuracy and robustness of the approach.

The well-known Bernstein polynomials are frequently used in signal representation, finite impulse response filter realization, computer-aided geometric design, and B-spline techniques. In this letter, a refinement of the Bernstein approximation scheme for complex exponentials, by making use of a judicious Lagrange interpolation scheme, is proposed. Applied to a general function, this approach leads to a new polynomial approximant, termed a multinomial Lagrange-Bernstein approximant, that performs better than the usual Bernstein approximant.

Frequency-domain rational macromodeling techniques have to be limited to relatively small frequency ranges or to a limited number of poles, mostly due to numerical issues. A pertinent problem in system modeling is therefore to come up with a global broad-band macromodel, given a number of piecewise rational, possibly disjoint, small-band models. We describe an effective implementation procedure, based on orthonormal bandlimited Kautz sequences. As a first step, we show how a truncated Kautz basis can be obtained directly from a judiciously chosen state-space description. Next, having incorporated the bandlimitedness requirement, we obtain imbeddable orthonormal bandlimited Kautz sequences. A numerical procedure for calculating the underlying bandlimited scalar products and Grammians, as applied to piecewise bandlimited state-space data, is implemented and tested

The Cohen-Posch-Zaparovanny class of positive time-frequency distributions is restricted to a Fourier subclass, and it is shown that besides invariance of the marginals, all members of this class exhibit the same entropy.

A generalization of the important Strang-Fix bound in the domain of L/sub 2/ interpolation and quasi-interpolation is presented. The results presented are obtained by straightforward and well-known operator and algebra norm techniques.

The zeros of predictor polynomials are shown to belong to the numerical range of a shift operator associated with the particular prediction problem under consideration. The numerical range consists of the classical field of values of the shift operator when the setting is Hilbert space, but a new definition is necessary when the setting is a general normed space. It is shown that a predictor polynomial is not stable in general. Nevertheless, for predictor polynomials in l/sub p/ spaces, it is shown that their zeros belong to the open circular disk with radius 2.>