A supernodal block factorized sparse approximate inverse for non-symmetric linear systems

2017 ◽  
Vol 78 (1) ◽  
pp. 333-354 ◽  
Author(s):  
Massimiliano Ferronato ◽  
Giorgio Pini
Keyword(s):  
Linear Systems ◽  
Approximate Inverse ◽  
Sparse Approximate Inverse

scholarly journals On the Relation between the AINV and the FAPINV Algorithms

2009 ◽  
Vol 2009 ◽  
pp. 1-6
Author(s):  
Davod Khojasteh Salkuyeh ◽  
Hadi Roohani
Keyword(s):  
Linear Systems ◽  
Systems Of Equations ◽  
Approximate Inverse ◽  
Sparse Approximate Inverse ◽  
Linear Systems Of Equations

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.

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