Partitioned Sparse A-1 Methods

This paper solves the classic Ax=b problem by constructing factored components of the inverses of L and U, the triangular factors of A. The number of additional fill-ins in the partitioned inverses of L and U can be made zero. The number of partitions is related to the path length of sparse vector methods. Allowing some fill-in in the partitioned inverses of L and U results in fewer partitions. Ordering algorithms most suitable for sparsity preservation in the inverses of L and U require additional fill-in in L and U themselves. Tests on practical power system matrices from 118 to 1993 nodes indicate that the proposed approach is competitive in serial environments, and appears more suitable for parallel environments. Because sparse vectors are not required, the approach works not only for shortcircuit calculations but also for power flow and stability computations. Kevwords: Power Flow, Stability, Parallel computing, Sparse Matrices, Linear equations, Partitioning.