Geodesic
A parallel algorithm for computing the group inverse via Perron complementation
The electronic journal of linear algebra, Tome 13 (2005), pp. 131-145.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: A parallel algorithm is presented for computing the group inverse of a singular M-matrix of the form A = I - T , where T 2 Rn*n is irreducible and stochastic. The algorithm is constructed in the spirit of Meyer's Perron complementation approach to computing the Perron vector of an irreducible nonnegative matrix. The asymptotic number of multiplication operations that is necessary to implement the algorithm is analyzed, which shows that the algorithm saves a significant amount of computation over the direct computation of the group inverse of A.
Classification : 15A09, 15A48, 15A51, 65F30, 65C40
Keywords: group inverses, M-matrices, perron complements, parallel algorithm 
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     author = {Neumann, Michael and Xu, Jianhong},
     title = {A parallel algorithm for computing the group inverse via {Perron} complementation},
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Neumann, Michael; Xu, Jianhong. A parallel algorithm for computing the group inverse via Perron complementation. The electronic journal of linear algebra, Tome 13 (2005), pp. 131-145. http://geodesic.mathdoc.fr/item/ELA_2005__13__a16/