(untitled) (Journal of Computational Mathematics, 2021)
The parallel arithmetic complexities for computing generalized inverse A^+, computing the minimum-norm least-squares solution of Ax=b, computing order m+n-r determinants and finding the characteristic polynomials of order m+n-r matrices are shown to have the same grawth rate. Algorithms are given that compute A^+ and A_MN^+ in O(rn+m) and O(^2n+m) steps using a number of processors which is a polynomial in m, n and r (AB_r^m× n,r=rank A).