Abstract
The approximate inverse (AINV) and the factored approximate inverse (FAPINV) are two known algorithms in the field of preconditioning of linear systems of equations. Both of these algorithms compute a sparse approximate inverse of matrix in the factored form and are based on computing two sets of vectors which are -biconjugate. The AINV algorithm computes the inverse factors and 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.
Highlights
Introduction1.1 where the coefficient matrix A ∈ Rn×n is nonsingular, large, sparse, and x, b ∈ Rn
Consider the linear system of equationsAx b, 1.1 where the coefficient matrix A ∈ Rn×n is nonsingular, large, sparse, and x, b ∈ Rn
We have shown that the AINV and FAPINV algorithms are strongly related
Summary
1.1 where the coefficient matrix A ∈ Rn×n is nonsingular, large, sparse, and x, b ∈ Rn. The factored approximate inverse FAPINV Lee and Zhang 6, 7 , Luo 8–10 , Zhang 11, 12 and the approximate inverse AINV see Benzi and Tuma 13, 14 are among the algorithms for computing an approximate inverse of A in International Journal of Mathematics and Mathematical Sciences the factored form. Both of these methods compute lower unitriangular matrices W and ZT and a diagonal matrix D diag d1, d2, .
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