Efficient computation of sparse approximate inverses

We investigate different methods for computing a sparse approximate inverse M for a given sparse matrix A by minimizing ∥AM − E∥ in the Frobenius norm. Such methods are very useful for deriving preconditioners in iterative solvers, especially in a parallel environment. We compare different strategies for choosing the sparsity structure of M and different ways for solving the small least squares problem that are related to the computation of each column of M. Especially we show how we can take full advantage of the sparsity of A. © 1998 John Wiley & Sons, Ltd.