On the Approximate Cyclic Reduction Preconditioner

Abstract

We present a preconditioning method for the iterative solution of large sparse systems of equations. The preconditioner is based on 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. A Schur complement approximation is constructed using a sequence of point-Gaussian elimination steps. The resulting preconditioner has a transparent modular structure similar to the algorithmic structure of a multigrid V-cycle.