Sparse Gaussian Elimination and Orthogonal Factorization

We consider the solution of a linear system Ax = b on a distributedmemorymachine when the matrixA has full rank and is large, sparse and nonsymmetric. We use our Cartesian nested dissection algorithm to compute a ll-reducingcolumn ordering of the matrix. We develop algorithms that use the associated separator tree to estimate the structure of the factor and to distribute and perform numeric computations. When the matrix is nonsymmetric but square, the numeric computations involve Gaussian elimination with row pivoting; when the matrix is overdetermined, row-oriented Householder transforms are applied to compute the triangular factor of an orthogonal factorization. We compare the ll incurred by our approach to that incurred by well known sequential methods and report on the performance of our implementation on the Intel iPSC/860.