TY - JOUR
T1 - Fast Parallel Algorithms for Computing Generalized Inverses $A^+$ and $A_{MN}^+$
AU - Wang , Guo-Rong
AU - Lu , Sen-Quan
JO - Journal of Computational Mathematics
VL - 4
SP - 348
EP - 354
PY - 1988
DA - 1988/06
SN - 6
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/9523.html
KW - 
AB - <p style="text-align: justify;">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 polynomial in $m, \ n$ and $r$ $(A\in B_r^{m\times n},r=rank \ A)$.</p>