An adaptive-order rational Arnoldi method for model-order reductions of linear time-invariant systems

This work proposes a model reduction method, the adaptive-order rational Arnoldi (AORA) method, to be applied to large-scale linear systems. It is based on an extension of the classical multi-point Padé approximation (or the so-called multi-point moment matching), using the rational Arnoldi iteration approach. Given a set of predetermined expansion points, an exact expression for the error between the output moment of the original system and that of the reduced-order system, related to each expansion point, is derived first. In each iteration of the proposed adaptive-order rational Arnoldi algorithm, the expansion frequency corresponding to the maximum output moment error will be chosen. Hence, the corresponding reduced-order model yields the greatest improvement in output moments among all reduced-order models of the same order. A detailed theoretical study is described. The proposed method is very appropriate for large-scale electronic systems, including VLSI interconnect models and digital filter designs. Several examples are considered to demonstrate the effectiveness and efficiency of the proposed method.