On the Relation between the AINV and the FAPINV Algorithms
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 𝐴 in the factored form and are based on computing two sets of...
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2009/179481 |
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| author | Davod Khojasteh Salkuyeh Hadi Roohani |
| author_facet | Davod Khojasteh Salkuyeh Hadi Roohani |
| author_sort | Davod Khojasteh Salkuyeh |
| collection | DOAJ |
| description | 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 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. |
| format | Article |
| id | doaj-art-da306ba98eb14aa4829789ad232f7555 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-da306ba98eb14aa4829789ad232f75552025-02-03T06:01:22ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252009-01-01200910.1155/2009/179481179481On the Relation between the AINV and the FAPINV AlgorithmsDavod Khojasteh Salkuyeh0Hadi Roohani1Department of Mathematics, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, IranDepartment of Mathematics, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, IranThe 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 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.http://dx.doi.org/10.1155/2009/179481 |
| spellingShingle | Davod Khojasteh Salkuyeh Hadi Roohani On the Relation between the AINV and the FAPINV Algorithms International Journal of Mathematics and Mathematical Sciences |
| title | On the Relation between the AINV and the FAPINV Algorithms |
| title_full | On the Relation between the AINV and the FAPINV Algorithms |
| title_fullStr | On the Relation between the AINV and the FAPINV Algorithms |
| title_full_unstemmed | On the Relation between the AINV and the FAPINV Algorithms |
| title_short | On the Relation between the AINV and the FAPINV Algorithms |
| title_sort | on the relation between the ainv and the fapinv algorithms |
| url | http://dx.doi.org/10.1155/2009/179481 |
| work_keys_str_mv | AT davodkhojastehsalkuyeh ontherelationbetweentheainvandthefapinvalgorithms AT hadiroohani ontherelationbetweentheainvandthefapinvalgorithms |