Abstract
Among the RC reduction algorithms, the algorithm of PACT (Pole Analysis via Congruence Transformations) [41 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 [4], 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.