Enhancing the efficiency of reduction of large RC networks by pole analysis via congruence transformations

Among the RC reduction algorithms, the algorithm of PACT (Pole Analysis via Congruence Transformations) has been proved to have several advantages. However, the original implementation of the algorithm destroys the sparsity of the internal capacitance matrix. Consequently, the LASO process, used in the computation of the dominant eigenvalues and eigenvectors, becomes very time-consuming. Therefore, the efficiency of the algorithm needs to be improved. In this paper, a new method to implement the PACT algorithm is presented. In order to maintain the sparsity of the matrices, we use a special Lanczos algorithm to directly compute the eigenvalues and eigenvectors by solving a large sparse symmetric generalized eigenvalue problem, At the same time, this approach can avoid some matrix multiplication to speed up the reduction process. We have constructed a RC reduction tool with the new implementation method. The application of the tools to several RC networks has shown that this tool greatly outperforms the original implementation.