ELA, Volume 13, pp. 131-145, April 2005, abstract.
A Parallel Algorithm For Computing The Group
Inverse Via Perron Complementation
Michael Neumann and Jianhong Xu
A parallel algorithm is presented for computing
the group inverse of a singular M-matrix of the
form A = I-T, where T is a real n-by-n matrix
that 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.