Self adaptive spectral conjugate gradient method for solving nonlinear monotone equations
Koorapetse, M., Kaelo, P. (2020). Self adaptive spectral conjugate gradient method for solving nonlinear monotone equations. EKB Journal Management System, 28(1), 1-21. doi: 10.1186/s42787-019-0066-1
M. Koorapetse; P. Kaelo. "Self adaptive spectral conjugate gradient method for solving nonlinear monotone equations". EKB Journal Management System, 28, 1, 2020, 1-21. doi: 10.1186/s42787-019-0066-1
Koorapetse, M., Kaelo, P. (2020). 'Self adaptive spectral conjugate gradient method for solving nonlinear monotone equations', EKB Journal Management System, 28(1), pp. 1-21. doi: 10.1186/s42787-019-0066-1
Koorapetse, M., Kaelo, P. Self adaptive spectral conjugate gradient method for solving nonlinear monotone equations. EKB Journal Management System, 2020; 28(1): 1-21. doi: 10.1186/s42787-019-0066-1

Self adaptive spectral conjugate gradient method for solving nonlinear monotone equations

Journal of the Egyptian Mathematical Society
Volume 28, Issue 1, June 2020, Pages 1-21    PDF (594.27 K)
DOI: 10.1186/s42787-019-0066-1
Authors
M. Koorapetse; P. Kaelo
Department of Mathematics, University of Botswana, Private Bag UB00704 Gaborone, Botswana
Abstract
In this paper, we propose a self adaptive spectral conjugate gradient-based projection
method for systems of nonlinear monotone equations. Based on its modest memory
requirement and its efficiency, the method is suitable for solving large-scale equations.
We show that the method satisfies the descent condition FT
k dk ≤ −cFk2, c > 0, and
also prove its global convergence. The method is compared to other existing methods
on a set of benchmark test problems and results show that the method is very efficient
and therefore promising.

Keywords
Self adaptive; Spectral conjugate gradient method; Nonlinear monotone equations
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