Abstract
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. Furthermore, we give assistance how to design and apply an algorithm for computing sparse approximate inverses for a general sparse matrix.
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