Ildl factorizations for sparse skew-symmetric matrices

Our goal is to solve a sparse skew-symmetric linear system efficiently. We propose a slight modification to the Bunch LDL\T factorization with partial pivoting strategy for skew-symmetric matrices, which saves approximately one third of the overall number of swaps of rows and columns on average. We also develop a rook pivoting strategy for this LDL\T factorization in Crout order. We derive an incomplete LDL\T factorization based on the full LDL\T factorization, with both partial pivoting strategy and rook pivoting strategy. The incomplete factorization can be used as a preconditioner for Krylov subspace solvers. Various column versions of ILUTP factorizations are investigated. We show that the approach taken saves approximately half of the work and storage compared to standard ILU factorizations that do not exploit the structure of the matrix, and the rook pivoting strategy is often superior to the partial pivoting strategy, in particular when the matrix is ill-conditioned and the overall number of elements in the rows of the factors is restricted.Science, Faculty ofComputer Science, Department ofGraduat