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Volume 13, Issue 4
On the Splittings for Rectangular Systems

H. J. Tian

J. Comp. Math., 13 (1995), pp. 337-342.

Published online: 1995-08

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  • Abstract

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 $x_0\in C^n$.

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@Article{JCM-13-337, author = {}, title = {On the Splittings for Rectangular Systems}, journal = {Journal of Computational Mathematics}, year = {1995}, volume = {13}, number = {4}, pages = {337--342}, abstract = {

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 $x_0\in C^n$.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9275.html} }
TY - JOUR T1 - On the Splittings for Rectangular Systems 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 -

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 $x_0\in C^n$.

H. J. Tian. (1970). On the Splittings for Rectangular Systems. Journal of Computational Mathematics. 13 (4). 337-342. doi:
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