A generalized projection iterative method for solving non-singular linear systems

Abstract

<p style='text-indent:20px;'>In this paper, we propose and analyze iterative method based on projection techniques to solve a non-singular linear system <inline-formula><tex-math id="M1">\begin{document}$ Ax = b $\end{document}</tex-math></inline-formula>. In particular, for a given positive integer <inline-formula><tex-math id="M2">\begin{document}$ m $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M3">\begin{document}$ m $\end{document}</tex-math></inline-formula>-dimensional successive projection method (<inline-formula><tex-math id="M446">\begin{document}$ m $\end{document}</tex-math></inline-formula>D-SPM) for symmetric positive definite matrix <inline-formula><tex-math id="M4">\begin{document}$ A $\end{document}</tex-math></inline-formula>, is generalized for non-singular matrix <inline-formula><tex-math id="M5">\begin{document}$ A $\end{document}</tex-math></inline-formula>. Moreover, it is proved that <inline-formula><tex-math id="M6">\begin{document}$ m $\end{document}</tex-math></inline-formula>D-SPM gives better result for large values of <inline-formula><tex-math id="M7">\begin{document}$ m $\end{document}</tex-math></inline-formula>. Numerical experiments are carried out to demonstrate the superiority of the proposed method in comparison with other schemes in the scientific literature.</p>