Approximate symbolic pole/zero extraction using equation-based simplification driven by eigenvalue shift prediction

This paper presents a new approach to symbolic pole/zero analysis of linear electronic circuits using equation-based simplification techniques driven by novel term ranking and error control strategies. Term rankings are determined by using a linear prediction formula to estimate the shifts of the eigenvalues of interest caused by removing terms from a matrix equation. The shift estimations are based on one initial solution of a numerical generalized eigenvalue problem. Error control is achieved by tracking the true eigenvalue shifts numerically. The algorithm allows for the computation of approximated symbolic expressions for selected poles and zeros, including non-dominant ones.