PARALLEL SPARSE-MATRIX SOLUTION AND PERFORMANCE

A parallel solution to the large sparse systems of linear equations is presented. The solution method is based on a parallel pivoting technique for LU decomposition on a shared memory MIMD multiprocessor. At each application of the algorithm to the matrix several pivots for reducing the matrix in parallel are generated. During parallel pivoting steps only symmetric permutations are possible. Unsymmetric permutation for numerical stability however is possible during single pivoting steps. We will report on switching between parallel and single pivoting steps to assure numerical stability. Once the matrix is decomposed, the parallel pivoting information is used to solve structurally identical matrices repeatedly. The algorithms, their implementation, and the performance of the solution methods on actual multiprocessors are presented. Based on the resulting triangular matrix structure, two algorithms for back substitution are presented and their performance is compared.