Improved Symbolic and Numerical Factorization Algorithms for Unsymmetric Sparse Matrices (original) (raw)

We present algorithms for the symbolic and numerical factorization phases in the direct solution of sparse unsymmetric systems of linear equations. We have modi ed a classical symbolic factorization algorithm for unsymmetric matrices to inexpensively compute minimal elimination structures. We give an e cient algorithm to compute a near-minimal data-dependency graph that is valid irrespective of the amount of dynamic pivoting performed during numerical factorization. Finally, we describe an unsymmetric-pattern multifrontal algorithm for Gaussian elimination with partial pivoting that uses the task-and data-dependency graphs computed during the symbolic phase. These algorithms have been implemented in WSMP|an industrial strength sparse solver package|and have enabled WSMP to signi cantly outperform other similar solvers. We present experimental results to demonstrate the merits of the new algorithms.