1999-01-12
16:15 at IFW A32

Sparse Approximate Inverses and Multigrid Methods

Thomas Huckle

Department of Informatics, TU Munich

We consider different sparse approximate inverses as smoother in multigrid methods. On the one hand we discuss the original SPAI and the SAI-method (by Tang and Wan) applied to the full matrices A_k. On the other hand we compare different factorized sparse approximate inverses, e.g. SPAI applied to the Gauss-Seidel smoother, AINV introduced by Benzi and Tuma, and the inverse Cholesky approximation (Kaporin, Kolotilina, Yeremin). Furthermore we discuss a-priori estimates for the sparsity pattern of sparse approximate inverses and present a formulation of Multigrid methods that can be very useful for designing sparse approximate inverses as smoothers.