About cookies on this site Our websites require some cookies to function properly (required). In addition, other cookies may be used with your consent to analyze site usage, improve the user experience and for advertising. For more information, please review your options. By visiting our website, you agree to our processing of information as described in IBM’sprivacy statement. To provide a smooth navigation, your cookie preferences will be shared across the IBM web domains listed here.
Paper
Improved symbolic and numerical factorization algorithms for unsymmetric sparse matrices
Abstract
We present algorithms for the symbolic and numerical factorization phases in the direct solution of sparse unsymmetric systems of linear equations. We have modified a classical symbolic factorization algorithm for unsymmetric matrices to inexpensively compute minimal elimination structures. We give an efficient 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 in WSMP - an industrial strength sparse solver package - and have enabled WSMP to significantly outperform other similar solvers. We present experimental results to demonstrate the merits of the new algorithms.