Modified matrix-free methods for solving system of nonlinear equations

References

• Dennis JE, Schnabel RB. Numerical methods for unconstrained optimization and nonlinear equations. Prentice hall, Englewood Cliffs, NJ. 1983.
   Google Scholar
• Waziri MY, Leong WJ, Hassan MA, et al. Jacobian computation-free Newton method for systems of non-linear equations. J Numer Math Stochast. 2010;2:54–63.
   Google Scholar
• Waziri MY, Majid ZA. An enhanced matrix-free secant mehod via predictor-corrector modified line search strategies for solving systems of nonlinear equations. J Math Math Sci. 2013. Article ID 814587: 6 pp. doi.org/https://doi.org/10.1155/2013/814587.
   Google Scholar
• Zang L, Zhou W, Li DH. Global convergence of modified Fletcher-Reeves conjugate gradient method with Armijo-type line search. Numerische Mathematik. 2005;164(1):277–289.
   Google Scholar
• Halilu AS, Waziri MY. En enhanced matrix-free method via double steplength approach for solving systems of nonlinear equations. Inter J Appl Math Res. 2017;6(4):147–156. doi.org/https://doi.org/10.14419/ijamr.v6i4.8072.
   Google Scholar
• Gonglin Y, Xiwen L. A new backtracking inexact BFGS method for symmetric nonlinear equations. J Comput Math Appl. 2008;55:116–129. doi: https://doi.org/10.1016/j.camwa.2006.12.081
   Web of Science ®Google Scholar
• Halilu AS, Waziri MY. An improved derivative-free method via double direction approach for solving systems of nonlinear equations. J Ramanujan Math Soc. 2018;33(1):75–89.
   Web of Science ®Google Scholar
• Petrović MJ, Stanimirović PS. Accelerated double direction method for solving unconstrained optimization problems. Math Probl Eng. 2014. Article ID 965104: 8 pp. doi.org/https://doi.org/10.1155/2014/965104.
   Google Scholar
• Li D, Fukushima M. A global and superlinear convergent Gauss-Newton based BFGS method for symmetric nonlinear equation. SIAM J Numer Anal. 1999;37:152–172. doi: https://doi.org/10.1137/S0036142998335704
   Web of Science ®Google Scholar
• Petrović MJ. An accelerated double step size model in unconstrained optimization. Appl Math Comput. 2015;250:309–319. doi.org/https://doi.org/10.1016/j.amc.2014.10.104.
   Web of Science ®Google Scholar
• Petrović MJ, Stanimirović PS, Kontrec N, et al. Hybrid modification of accelerated double direction method. Math Probl Eng. 2018. Article D 1523267: 8 pp. doi.org/https://doi.org/10.1155/2018/1523267.
   Google Scholar
• Petrović MJ. Hybridization rule applied on accelerated double step size optimization scheme. Filomat. 2019;33(3):655–665. doi.org/https://doi.org/10.2298/FIL1903655P.
   Web of Science ®Google Scholar
• Petrović MJ, Rakoević V, Valjarević D, et al. A note on hybridization process applied on transformed double step size model. Numer Algor. 2019. doi.org/https://doi.org/10.1007/s11075-019-00821-8.
   Google Scholar
• Panić S, Petrović MJ, Carević MM. Initial improvement of the hybrid accelerated gradient descent process. Bull Aust Math Soc. 2018;98(2):331–338. doi.org/https://doi.org/10.1017/S0004972718000552.
   Web of Science ®Google Scholar
• Safeer HK. A Picard-Mann hybrid iterative process. Khan Fixed Point Theory Appl. 2013;69:10.
   Google Scholar
• Andrei N. A hybrid conjugate gradient algorithm for unconstrained optimization as a convex combination of Hestenes-Stiefel and Dai-Yuan. Stud Inform Control. 2008;17(4):55–70.
   Web of Science ®Google Scholar
• Babaie-Kafaki S, Ghanbari SR. Two hybrid nonlinear conjugate gradient methods based on a modified secant equation. Optimization. 2014;63(7):1027–1042. doi: https://doi.org/10.1080/02331934.2012.693083
   Web of Science ®Google Scholar
• Li JK, Liu SJ. New hybrid conjugate gradient method for unconstrained optimization. Appl Math Comput. 2014;245:36–43.
   Web of Science ®Google Scholar
• Petrović M, Rakočević V, Kontrec N, et al. Hybridization of accelerated gradient descent method. Numer Algor. 2017;79(3):769–786. doi.org/https://doi.org/10.1007/s11075-017-0460-4.
   Web of Science ®Google Scholar
• Stanimirović PS, Miladinović MB. Accelerated gradient descent methods with line search. Numer Algor. 2010;54:503–520. doi.org/https://doi.org/10.1007/s11075-009-9350-8.
   Web of Science ®Google Scholar
• Halilu AS, Waziri MY, Musa YB. Inexact double step length method for solving systems of nonlinear equations. Stat Optim Inf Comput. 2020;8:165–174. doi:https://doi.org/10.19139/soic-2310-5070-532.
   Google Scholar
• Halilu AS, Waziri MY, Yusuf I. Efficient matrix-free direction method with line search for solving large-scale system of nonlinear equations. Yugoslav J Oper Res. doi.org/https://doi.org/10.2298/YJOR160515005H.
   Google Scholar
• Barzilai J, Borwein JM. Two point step size gradient method. IMA J Numer Anal. 1988;8(1):141–148. doi.org/https://doi.org/10.1093/imanum/8.1.141.
   Web of Science ®Google Scholar
• Halilu AS, Waziri MY. A transformed double steplength method for for solving large-scale systems of nonlinear equations. J Numer Math Stochastics. 2017;9(1):20–23.
   Google Scholar
• Waziri MY, Ahmed K, Sabi'u J. A family of Hager–Zhang conjugate gradient methods for system of monotone nonlinear equations. Appl Math Comput. 2019;361:645–660.
   Web of Science ®Google Scholar
• La Cruz W, Martinez JM, Raydan M. spetral residual method without gradient information for solving large-scale nonlinear systems of equations: theory and experiments. P Optim. 2006;75(225):1429–1448.
   Google Scholar
• Abubakar AB. On improved Broyden-type method for systems of nonlinear equations [M.Sc. Thesis BUk]. 2014. 1–54.
   Google Scholar
• Halilu AS, Dauda MK, Waziri My, et al. A derivative-free decent method via acceleration parameter for solving systems of nonlinear equations . Open J sci. tech. 2019;2(3):1–4. doi: https://doi.org/10.31580/ojst.v2i3.931
   Google Scholar
• Stanimirović PS, Milovanović GV, Petrović MJ, et al. A transformation of accelerated double step size method for unconstrained optimization. Math Probl Eng. 2015; Article ID 283679: 8 pp. https://doi.org/10.1155/2015/283679.
   Google Scholar
• Dolan E, More J. Benchmarking optimization software with performance profiles. J Math Program. 2002;91(2):201–213. doi: https://doi.org/10.1007/s101070100263
   Web of Science ®Google Scholar
• Waziri MY, Sabiu J. A derivative-free conjugate gradient method and its global convergence for symmetric nonlinear equations. J Math Mathematical Sc. 2015; Article ID 961487: 8 pp.
   Google Scholar