International Journal of Mathematics and Computer Science, 17(2022), no. 3, 1193–1199 M CS A Refinement of the KSOR Iterative Method Sh. A. Meligy 1 , I. K. Youssef 2 1 Department of Basic Engineering Sciences Faculty of Engineering at Shoubra Benha University Cairo, Egypt 2 Department of Mathematics Faculty of Science Ain Shams University Cairo, Egypt and Department of Mathematics College of Science Islamic University Madinah, Saudi Arabia email: shaban.mahmoud@feng.bu.edu.eg, kaoud22@sci.asu.edu.eg (Received March 1, 2022, Accepted April 4, 2022) Abstract We introduce a refinement formulation of the KSOR method and establish the rate of convergence of the introduced formulas. We com- pare a new formula (RKSOR) with the classical form (KSOR). The efficient performance of the new form is established theoretically and confirmed through a numerical example. The decrease in the required number of iterations for convergence is established through the calcu- lation of the spectral radius of the iteration matrices. The calculations and graphs are performed with the help of the computer algebra soft- ware Mathematica. Key words and phrases: Linear systems, KSOR method, iterative and refinement technique. AMS (MOS) Subject Classifications: 65F10, 15A06, 15A30. ISSN 1814-0432, 2022, http://ijmcs.future-in-tech.net