Code orderings for the solution of sparse positive definite linear systems Original Research Article

Direct methods based on the loop-free approach for the solution of sparse linear systems have been left aside for the last two decades due to their excessive demand on computational resources. In the solution of successive systems with the same structural nonzero element pattern, the exploitation of coding techniques and implicit reordering schemes presented in this work, leads to new classes of implementable alternatives to the loop-free approach. Some of the techniques can also be applied to iterative solvers pre-conditioned by incomplete factorization schemes, increasing their efficiency at sparse matrix×vector operations, and dynamic drop of elements.