A New Method for Ordering Sparse Matrices and Its Performance in Circuit Simulation

Local algorithms for obtaining a pivot ordering for sparse symmetric coefficient matrices are reviewed together with their mathematical background and appropriate data structures. Recently proposed heuristics as well as improvements to them are discussed, and their performance, mainly in terms of the resulting number of factorization operations, is compared with that of the Minimum Degree and the Minimum Local Fill algorithms. It is demonstrated that a combination of Markowitz’ algorithm with these symmetric methods applied to the unsymmetric matrices arising in circuit simulation is capable of accelerating the simulation significantly.