Error estimations of Arnoldi-based interconnect model-order reductions

Projection-based model reductions become a necessity for efficient interconnect modeling and simulations. In order to choose the order of the reduced system that can really reflect the essential dynamics of the original interconnect, the residual error of the transfer function can be considered as a stopping criteria to terminate the Arnoldi iteration process. Analytical expressions of this residual error are derived in detail. Furthermore, it can be found that the approximate transfer function can also be expressed as the original interconnect model with some additive perturbations. The perturbation matrix only involves resultant vectors at the previous step of the Arnoldi algorithm. These error information will provide a guideline for the order selection scheme used in the Krylov subspace model-order algorithm.