Volume 55, Number 6, November-December 2021
|Page(s)||3293 - 3316|
|Published online||15 November 2021|
On the derivative-free quasi-Newton-type algorithm for separable systems of nonlinear equations
Department of Mathematical Sciences, Faculty of Physical Sciences, Bayero University, Kano, Nigeria
2 Numerical Optimization Research Group, Bayero University, Kano, Nigeria
3 Department of Mathematics, Faculty of Science, Gombe State University, Gombe, Nigeria
4 KMUTT Fixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok, 10140, Thailand
5 Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, Pretoria, Medunsa 0204, South Africa
6 Department of Computer Science, Federal College of Agricultural Produce Technology, Kano, Nigeria
* Corresponding author: firstname.lastname@example.org
Accepted: 9 October 2021
A derivative-free quasi-Newton-type algorithm in which its search direction is a product of a positive definite diagonal matrix and a residual vector is presented. The algorithm is simple to implement and has the ability to solve large-scale nonlinear systems of equations with separable functions. The diagonal matrix is simply obtained in a quasi-Newton manner at each iteration. Under some suitable conditions, the global and R-linear convergence result of the algorithm are presented. Numerical test on some benchmark separable nonlinear equations problems reveal the robustness and efficiency of the algorithm.
Mathematics Subject Classification: 65K05 / 65H10 / 90C30 / 90C53
Key words: Separable nonlinear equations / derivative-free methods / quasi-Newton-type methods / convergence / numerical experiments
© The authors. Published by EDP Sciences, ROADEF, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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