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Vector Fitting is a popular method of constructing rational approximantsdesigned to fit given frequency response measurements. The original method,which we refer to as VF, is based on a least-squares fit to the measurements bya rational function, using an iterative reallocation of the poles of theapproximant. We show that one can improve the performance of VF significantly,by using a particular choice of frequency sampling points and properlyweighting their contribution based on quadrature rules that connect the leastsquares objective with an H2 error measure. Our modified approach, designatedhere as QuadVF, helps recover the original transfer function with better globalfidelity (as measured with respect to the H2 norm), than the localized leastsquares approximation implicit in VF. We extend the new framework also toincorporate derivative information, leading to rational approximants thatminimize system error with respect to a discrete Sobolev norm. We consider theconvergence behavior of both VF and QuadVF as well, and evaluate potentialnumerical ill-conditioning of the underlying least-squares problems. Weinvestigate briefly VF in the case of noisy measurements and propose a newformulation for the resulting approximation problem. Several numerical examplesare provided to support the theoretical discussion.

Quadrature-Based Vector Fitting: Implications For H2 System Approximation