Some remarks on the Vector Fitting iteration

Vector Fitting (VF) is an iterative technique to construct rational approximations based on multiple frequency domain samples, introduced by Gustavsen and Semlyen [1, 3]. VF is nowadays widely investigated and used in the Power Systems and Microwave Engineering communities. Numerical experiments show that VF has favorable convergence properties. However, so far, no theoretical proof for its convergence, or conditions to guarantee convergence, have been published. This paper gives a description of a general iterative Least-Squares framework for rational approximation and shows that VF fits into this framework.