On the Nonconvergence of the Vector Fitting Algorithm

The vector fitting (VF) algorithm, as a variant of the Sanathanan-Koerner (SK) algorithm, has been widely used for frequency-domain modeling. This algorithm is essentially an iterative procedure, in which a revised linear least squares (LS) problem is solved in each step. So far, there has been hardly any analytical result in the literature on the convergence property of the SK or the VF algorithm. In this brief, several results are developed. First, it is shown that, if the frequency response data are noisy, then the SKor the VF algorithm, if it converges, would never reach any local minimum of the original nonlinear LS problem. Second, by modeling the SK or the VF algorithm as a sequence of solving weighted LS problems with updated weights, it is shown that, with noisy data, the SK or the VF algorithm, if it converges, would never reach any stationary point with respect to weights. With regard to the general convergence, a counterexample is given to show that the SK or the VF algorithm does not converge and, in fact, runs into limit-cycle-like oscillation.