Ordering, Anisotropy, and Factored Sparse Approximate Inverses

Ordering, Anisotropy, and Factored Sparse Approximate Inverses

We consider ordering techniques to improve the performance of factored sparse approximate inverse preconditioners, concentrating on the AINV technique of M. Benzi and M. Tůma. Several practical existing unweighted orderings are considered along with a new algorithm, minimum inverse penalty (MIP), that we propose. We show how good orderings such as these can improve the speed of preconditioner c...

On the Relations between ILUs and Factored Approximate Inverses

This paper discusses some relationships between Incomplete LU (ILU) factoriza-tion techniques and factored sparse approximate inverse (AINV) techniques. While ILU factorizations compute approximate LU factors of the coeecient matrix A, AINV techniques aim at building triangular matrices Z and W such that W > AZ is approximately diagonal. The paper shows that certain forms of approximate inverse...

Sparse Approximate Inverses and Target Matrices

Algebraic Multilevel Methods and Sparse Approximate Inverses

In this paper we introduce a new approach to algebraic multilevel methods and their use as preconditioners in iterative methods for the solution of symmetric positive definite linear systems. The multilevel process and in particular the coarsening process is based on the construction of sparse approximate inverses and their augmentation with corrections of smaller size. We present comparisons o...

Efficient computation of sparse approximate inverses