MIMO interconnects order reductions by using the multiple point adaptive-order rational global arnoldi algorithm

We extend the adaptive-order rational Arnoldi algorithm for multiple-inputs and multiple-outputs (MIMO) interconnect model order reductions. Instead of using the standard Arnoldi algorithm for the SISO adaptive-order reduction algorithm (AORA), we study the adaptive-order rational global Arnoldi (AORGA) algorithm for MIMO model reductions. In this new algorithm, the input matrix is treated as a vector form. A new matrix Krylov subspace, generated by the global Arnoldi algorithm, will be developed by a Frobenius-orthonormal basis. By employing congruence transformation with the matrix Krylov subspace, the one-sided projection method can be used to construct a reduced-order system. It will be shown that the system moment matching can be preserved. In addition, we also show that the transfer matrix residual error of the reduced system can be derived analytically. This error information will provide a guideline for the order selection scheme. The algorithm can also be applied to the classical multiple point MIMO Padé approximation by the rational Arnoldi algorithm for multiple expansion points. Experimental results demonstrate the feasibility and the effectiveness of the proposed method.