Sparse Matrix Ordering Algorithms

Abstract

AbstractSo far, our focus has been on the theoretical and algorithmic principles involved in sparse Gaussian elimination-based factorizations. To limit the storage and the work involved in the computation of the factors and in their use during the solve phase it is generally necessary to reorder (permute) the matrix before the factorization commences. The complexity of the most critical steps in the factorization is highly dependent on the amount of fill-in, as can be seen from the following observation.