Document Type : Research Article
Authors
1
Department of Mathematics, Sule Lamido university, Kafin Hausa, Nigeria.
2
Department of Mathematics, Northwest University, Kano, Nigeria.
3
Department of Mathematics, Northwest University, Kano, Nigeria
4
Department of mathematics, Sule Lamido University, Kafin Hausa, Nigeria.
5
Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Campus Besut, 22200 Terengganu, Malaysia.
6
3Department of Mathematics, Federal University, Dutse, Nigeria
7
College of Applied and Health Science, A’Sharqiyah University, No. 42, Postcode 400 Ibra, Sultanate of Oman
10.22067/ijnao.2026.100103.1920
Abstract
In this paper, we present a hybrid iterative algorithm for solving large-scale systems of nonlinear equations by combining an improved matrix-free method and a new iterative scheme. The proposed approach aims to improve computational efficiency without explicitly evaluating and storing the Jacobian matrix, and thus is particularly suitable for large-scale problems. The acceleration parameter for approximating the Jacobian matrix is obtained via a Taylor series expansion, thereby improving the quality of the search direction. Furthermore, the step length is determined by an inexact line search strategy to improve the convergence behaviour and the global stability of the algorithm. It is proved that the proposed method is globally convergent under suitable assumptions. The efficiency of the algorithm is confirmed by extensive numerical experiments on a set of benchmark nonlinear problems. Numerical experiments illustrate the efficiency and robustness of the proposed method and show that the proposed method is competitive with the existing matrix-free methods for solving large-scale systems of nonlinear equations.
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