On the approximate cyclic reduction preconditioner

We present a preconditioning method for the iterative solution of large spa rse systems of equations. The preconditioner is based on ideas both from IL U preconditioning and from multigrid. The resulting preconditioning techniq ue requires the matrix only. A multilevel structure is obtained by using ma ximal independent sets for graph coarsening. A Schur complement approximati on is constructed using a sequence of point-Gaussian elimination steps. The resulting preconditioner has a transparent modular structure similar to th e algorithmic structure of a multigrid V-cycle.