TY - JOUR
T1 - On the Splittings for Rectangular Systems
AU - H. J. Tian
JO - Journal of Computational Mathematics
VL - 4
SP - 337
EP - 342
PY - 1995
DA - 1995/08
SN - 13
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/9275.html
KW - 
AB - <p style="text-align: justify;">Recently, M. Hanke and M. Neumann$^{[4]}$ have derived a necessary and sufficient condition on a splitting of $A=U-V$, which leads to a fixed point system, such that the iterative sequence converges to the least squares solution of minimum 2-norm of the system $Ax=b$. In this paper, we give a necessary and sufficient condition on the splitting such that the iterative sequence converges to the weighted Moore-Penrose solution of the system $Ax=b$ for every $x_0\in C^n$ and every $b\in C^m$. We also provide a necessary and sufficient condition such that the iterative sequence is convergent for every $x_0\in C^n$.</p>