Perturbation approach for order selections of two-sided oblique projection-based interconnect reductions

An order selection scheme for two-sided oblique projection-based interconnect reduction will be investigated. It will provide a guideline for terminating the conventional nonsymmetric Padé via Lanczos (PVL) iteration process. By exploring the relationship of the system Grammians of the original network and those of the reduced network, it can be shown that the system matrix of the reduced-order system generated by the two-sided oblique projection can also be expressed as those of the original interconnect model with some additive perturbations. The perturbation matrix only involves bi-orthogonal vectors at the previous step of the nonsymmetric Lanczos algorithm. This perturbation matrix will provide the stopping criteria in the order selection scheme and achieve the desired accuracy of the approximate transfer function.