J. Comp. Math., 6 (1988), pp. 348-354. Fast Parallel Algorithms For Computing Generalized Inverses $A^+$ And $A_{MN}^+$ Guo-rong Wang 1, Sen-quan Lu 11 Shanghai Teachers' University, Shanghai, China Received 1987-3-21 Revised Online 2006-12-7 Abstract 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 $O(\log r\dot \log n+\log m)$ and $O(\log^2n+\log m)$ steps using a number of processors which is a ploynomial in m,n and r $(A\in B_r^{m\times n},r=rank A)$. Key words: