OPTIMAL PARALLEL SOLUTION OF SPARSE TRIANGULAR SYSTEMS

This paper considers the parallel solution of a sparse system Lx = b with triangular matrix L, which is often a performance bottleneck in parallel computation. When many systems with the same matrix are to be solved, the parallel efficiency can be improved by representing the inverse of L as a product of a few sparse factors. The factorization with the smallest number of factors is constructed, subject to the requirement that no new nonzero elements are created. Applications are to iterative solvers with triangular preconditioners, to structural analysis, or to power systems applications. Experimental results on the Connection Machine show the method to be highly valuable.