Multipoint Pade approximation using a rational block Lanczos algorithm

Abstract

This paper presents a general rational block Lanczos algorithm for computing multipoint matrix Pade approximation of linear multiport networks, which model many important circuits in digital, analog, or mixed signal designs. This algorithm generalizes a novel block Lanczos algorithm with a reliable adaptive scheme for breakdown treatment to address two drawbacks of the single frequency Pade approximation: poor approximation of the transfer function in the frequency domain far away from the expansion point and the instability of the reduced model when the original system is stable. In addition, due to smaller Krylov subspace corresponding to each frequency point, the rational algorithm also alleviates the possible breakdowns when computing high order approximations. The cost of full backward orthogonalization with respect to all previous Lanczos vectors in a rational Lanczos algorithm, as compared to a partial backward orthogonalization in a single point Lanczos algorithm, is offset by more accurate and smaller order approximations.