Combining rational interpolation with the vector fitting method

In this paper, a method is proposed to improve the initial poles and convergence of the vector fitting method. The procedure takes advantage of the robustness of the rational interpolation method in extracting stable poles over partitioned bandwidth and the numerical stability and fast convergence of the vector fitting method in generating accurate high-order rational approximation. First, the stable poles of the entire frequency range are obtained by partitioning the domain and performing rational interpolation in each bandwidth. Then, the collected poles are used as initial poles to the vector-fitting algorithm to obtain the overall high-order rational approximation. The accuracy and convergence of the standard vector fitting and proposed methods are compared. Examples are provided to demonstrate the advantage of the proposed approach.