Newton Method with Iddm

Year 2025, Volume: 13 Issue: 2, 305 - 308, 31.10.2025

Zeliha Özdemir Özbek , Gülnur Çelik Kızılkan , Kemal Aydın

Abstract

Newton method is an iterative method that used to solve the equation system by converting the nonlinear system into a linear algebraic equation system (SLAE). Although this method is generally the preferred method, there are some difficulties with it. One of these difficulties is that Newton method needs a solver for the system of linear equations along with it. In this paper, we presented the Newton method with Iddm using the iterative decreasing dimension method (Iddm) at this stage of the Newton method.

Keywords

Iterative decreasing dimension method , linear equation system , nonlinear equation systems , Newton method

References

• [1] Remani C.,Numerical methods for solving systems of nonlinear equations, Lakehead University Thunder Bay, Ontario, Canada, 2013.
• [2] Burden, R. L. and Faires, J. D., Numerical analysis, Ninth Edition, Cengage learning, 2015.
• [3] Keskin U˘ lker T.,The algorithm of decreasing dimension for the systems of linear algebraic equation, Master Thesis, Selc¸uk University Graduate Natural and Applied Sciences, Konya, 2004 (in Turkish), 2005.
• [4] Keskin, T. and Aydın, K., Iterative decreasing dimension algorithm, Comput. Math. Appl., vol:53, No.7 (2007), 1153-1158.
• [5] Ben-Israel, A., A Newton-Raphson method for the solution of systems of equations. J. Math. Anal. Appl., vol:15, No.2 (1966), 243-252.
• [6] Ortega, J. M. and Rheinboldt, W. C., Iterative solution of nonlinear equations in several variables, Society for Industrial and Applied Mathematics, 1970. [7] O¨ zdemir, Z., Iterative decreasing dimension algorithm for the solutions of differential equation systems, Master Thesis, Selc¸uk University Graduate Natural and Applied Sciences, Konya (in Turkish), 2022.