Improved Gradient Descent Iterations for Solving Systems of Nonlinear Equations
Predrag S. Stanimirović,
Bilall I. Shaini,
Jamilu Sabi’u,
Abdullah Shah,
Milena J. Petrović,
Branislav Ivanov,
Xinwei Cao,
Alena Stupina,
Shuai Li
Affiliations
Predrag S. Stanimirović
Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18000 Niš, Serbia
Bilall I. Shaini
Department of Mathematics, Faculty of Applied Sciences, State University of Tetova, St. Ilinden, n.n., 1220 Tetovo, North Macedonia
Jamilu Sabi’u
Department of Mathematics, Yusuf Maitama Sule University, Kano 700282, Nigeria
Abdullah Shah
Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
Milena J. Petrović
Faculty of Sciences and Mathematics, University of Pristina in Kosovska Mitrovica, Lole Ribara 29, 38220 Kosovska Mitrovica, Serbia
Branislav Ivanov
Technical Faculty in Bor, University of Belgrade, Vojske Jugoslavije 12, 19210 Bor, Serbia
Xinwei Cao
School of Business, Jiangnan University, Lihu Blvd, Wuxi 214122, China
Alena Stupina
Laboratory “Hybrid Methods of Modelling and Optimization in Complex Systems”, Siberian Federal University, Prosp. Svobodny 79, 660041 Krasnoyarsk, Russia
Shuai Li
Faculty of Science and Engineering, Zienkiewicz Centre for Computational Engineering, Swansea University, Swansea SA1 8EN, UK
This research proposes and investigates some improvements in gradient descent iterations that can be applied for solving system of nonlinear equations (SNE). In the available literature, such methods are termed improved gradient descent methods. We use verified advantages of various accelerated double direction and double step size gradient methods in solving single scalar equations. Our strategy is to control the speed of the convergence of gradient methods through the step size value defined using more parameters. As a result, efficient minimization schemes for solving SNE are introduced. Linear global convergence of the proposed iterative method is confirmed by theoretical analysis under standard assumptions. Numerical experiments confirm the significant computational efficiency of proposed methods compared to traditional gradient descent methods for solving SNE.
