LU-Decomposition with Iterative Refinement for Solving Sparse Linear Systems

In the solution of a system of linear algebraic equations Ax = b with a large sparse coefficient matrix A, the LU-decomposition with iterative refinement (LUIR) is compared with the LU-decomposition with direct solution (LUDS), which is without iterative refinement. We verify by numerical experiments that the use of sparse matrix techniques with LUIR may result in a reduction of both the computing time and the storage requirements. The Powers of a Boolean Matrix Strategy (PBS) is used in an effort to achieve such a reduction and in an attempt to control the sparsity. We conclude that iterative refinement procedures may be efficiently used as an option in software for the solution of sparse linear systems of equations.