An approximate cyclic reduction multilevel preconditioner for general sparse matrices

We discuss an iterative method for solving large sparse systems of equations. A hybrid method is introduced which uses ideas both from ILU preconditioning and from multigrid. The resulting preconditioning technique requires the matrix only. A multilevel structure is obtained by using maximal independent sets for graph coarsening. For Schur complement approximation on coarser graphs an incomplete Gaussian elimination is used. The resulting preconditioner has a transparant modular structure similar to the algoritmic structure of a multigrid V-cycle.