PSOLVE : A Concurrent Algorithm for Solving Sparse Systems of Linear Equations

PSolve solves a sparse system of linear equations on a shared-memory parallel processor. Each autonomous process reduces a pair of matrix rows, uses pairwise pivoting for numerical stability, and synchronizes with only a few others at a time. For most test matrices, on the Alliant FX/8 multiprocessor, PSolve is faster than Gaussian Elimination (does not exploit sparsity) and the Yale Sparse Matrix Package (does not exploit parallelism). Although Gaussian Elimination runs in vector mode, PSolve cannot use currently available vector hardware because of its compact matrix storage scheme. However, with a new ''sparse-align'' vector unit, PSolve is vectorizable and runs faster than any other algorithm for all the selected test matrices. 11 refs., 10 figs.