Open Access
Issue
RAIRO-Oper. Res.
Volume 58, Number 1, January-February 2024
Page(s) 989 - 1003
DOI https://doi.org/10.1051/ro/2023117
Published online 04 March 2024
  • I.A. Al-Subaihi, Three-Step iterative method for solving nonlinear equations. Univers. J. Math. Appl. 3 (2015) 29–33. [CrossRef] [Google Scholar]
  • N. Andrei, An accelerated gradient descent algorithm with backtracking for unconstrained optimization. Numer. Algorithms 42 (2006) 63–73. [CrossRef] [MathSciNet] [Google Scholar]
  • J. Barzilai and J.M. Borwein, Two point step size gradient method. IMA J. Numer. Anal. 8 (1988) 141–148. [CrossRef] [MathSciNet] [Google Scholar]
  • A. Cauchy, Methodes generales pour la resolution des systemes dequations simultanees. C.R. Acad. Sci. Par. 25 536–538. [Google Scholar]
  • E. Dolan and J.J. Moré, Benchmarking optimization software with performance profiles. Math. Program. 91 (2002) 201–213. [CrossRef] [MathSciNet] [Google Scholar]
  • R. Fletcher and C. Reeves, Function minimization by conjugate gradients. Comput. J. 7 (1964) 149–154. [CrossRef] [MathSciNet] [Google Scholar]
  • A.S. Halilu and M. Waziri, En enhanced matrix-free method via double steplength approach for solving systems of nonlinear equations. Int. J. Appl. math. Res. 6 (2017) 147–156. [CrossRef] [Google Scholar]
  • A.S. Halilu and M. Waziri, An improved derivative-free method via double direction approach for solving systems of nonlinear equations. J. Ramanujan Math. Soc. 33 (2018) 75–89. [MathSciNet] [Google Scholar]
  • A.S. Halilu, M.Y. Waziri, H. Abdullahi and A. Majumder, On the hybridization of the double step length method for solving system of nonlinear equations. Malays. J. Math. Sci. 16 (2022) 329–349. [CrossRef] [MathSciNet] [Google Scholar]
  • S. Ishikawa, Fixed points by a new iteration method. Proc. Am. Math. Soc. 44 (1974) 147–150. [CrossRef] [Google Scholar]
  • W. La Cruz, J.M. Martínez and M. Raydan, Spectral residual method without gradient information for solving large-scale nonlinear systems of equations. Math. Comput. 75 (2006) 1429–48. [CrossRef] [Google Scholar]
  • D. Li and M. Fukushima, A global and superlinear convergent Gauss-Newton based BFGS method for symmetric nonlinear equation. SIAM J. Numer. Anal. 37 (1999) 152–172. [CrossRef] [MathSciNet] [Google Scholar]
  • M.A. Noor and M. Waseem, Some iterative methods for solving a system of nonlinear equations. Comput. Math. Appl. 57 (2009) 101–106. [MathSciNet] [Google Scholar]
  • M.J. Petrović, An Accelerated double step size model in unconstrained optimization, Appl. Math. Comput. 250 (2015) 39–319. [Google Scholar]
  • M.J. Petrović and P.S. Stanimirović, Accelerated double direction method for solving unconstrained optimization problems. Math. Probl. Eng. DOI: 10.1155/2014/965104 (2014). [Google Scholar]
  • M.J. Petrović, V. Rakoc̆ević, N. Kontrec, S. Panić and D. Ilić, Hybridization of accelerated gradient descent method. Numer. Algorithms 79 (2018) 769–786. [CrossRef] [MathSciNet] [Google Scholar]
  • E. Polak and G. Ribière, Note sur la convergence de méthodes de directions conjugues. Rev. Fr. Inform. Rech. Oper. 16 (1969) 35–43. [Google Scholar]
  • V. Rakoc̀ević and M.J. Petrović, Comparative analysis of accelerated models for solving unconstrained optimization problems with application of Khan’s hybrid rule. Mathematics 10 (2022). [Google Scholar]
  • H.K. Safeer, A Picard-Mann hybrid iterative process, Khan fixed point theory and applications (2013) 69. [Google Scholar]
  • P.S. Stanimirović and M.B. Miladinović, Accelerated gradient descent methods with line search. Numer. Algorithms 54 (2010) 503–520. [CrossRef] [MathSciNet] [Google Scholar]
  • M.Y. Waziri and Z.A. Majid, An enhanced matrix-free secant method via predictor-corrector modified line search strategies for solving systems of nonlinear equations. Int. J. Math. Math. Sci. (2013) 6. [Google Scholar]
  • M.Y. Waziri, W.J. Leong, M.A. Hassan and M. Monsi, Jacobian computation-free Newton method for systems of non-linear equations. J. Numer. Math. Stoch. 2 (2010) 54–63. [MathSciNet] [Google Scholar]
  • M.Y. Waziri, K. Ahmed and J. Sabi’u, A family of Hager–Zhang conjugate gradient methods for system of monotone nonlinear equations. Appl. Math. Comput. 361 (2019) 645–660. [CrossRef] [MathSciNet] [Google Scholar]

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