Improved Symbolic and Numerical Factorization Algorithms for Unsymmetric Sparse Matrices

W e present algorithms for the symbolic and numerical factorization phases in the direct solution of sparse unsymmetric systems of linearequations.W e have modified a classical symbolic factorization algorithm for unsymmetric matrices to inexpensively compute minimal elimination structures.W e give an e#cient algorithm to compute a near-minimal data-dependency graph for unsymmetric multifrontal factorization that is valid irrespective of the amount of dynamic pivoting performed during 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 inW.413X industrial strength sparse solver package---and have enabledWab to significantly outperform other similar solvers.W e present experimental results to demonstrate the merits of the new algorithms. Ke words. sparse matrix factorization, parallel sparse solvers, multifrontal methods AMS sub je2 classifications. 05C50, 65F05, 65F50, 65Y05 PII. S089547980139604X 1