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On the relation between the AINV and the FAPINV algorithms. (English) Zbl 1188.65030

Summary: The approximate inverse (AINV) and the factored approximate inverse (FAPINV) are two known algorithms in the field of preconditioning of systems of linear equations. Both of these algorithms compute a sparse approximate inverse of a matrix \(A\) in the factored form and are based on computing two sets of vectors which are \(A\)-biconjugate. The AINV algorithm computes the inverse factors \(W\) and \(Z\) of a matrix independently of each other, as opposed to the AINV algorithm, where the computations of the inverse factors are done independently. In this paper, we show that, without any dropping, removing the dependence of the computations of the inverse factors in the FAPINV algorithm results in the AINV algorithm.

MSC:

65F08 Preconditioners for iterative methods
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References:

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