Geodesic
Efficient Matrix-Free Direction Method With Line Search for Solving Large-Scale System of Nonlinear Equations
Yugoslav journal of operations research, Tome 30 (2020) no. 4, p. 399 .

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We proposed a matrix-free direction with an inexact line search technique to solve system of nonlinear equations by using double direction approach. In this article, we approximated the Jacobian matrix by appropriately constructed matrix-free method via acceleration parameter. The global convergence of our method is established under mild conditions. Numerical comparisons reported in this paper are based on a set of large-scale test problems and show that the proposed method is efficient for large-scale problems.
Classification : 65K05, 90C53, 65D32, 34G20
Keywords: Acceleration Parameter, Matrix-free, Inexact Line Search, Jacobian Matrix 
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     author = {Abubakar Sani Halilu and Mohammed Yusuf Waziri and Ibrahim Yusuf},
     title = {Efficient {Matrix-Free} {Direction} {Method} {With} {Line} {Search} for {Solving} {Large-Scale} {System} of {Nonlinear} {Equations}},
     journal = {Yugoslav journal of operations research},
     pages = {399 },
     publisher = {mathdoc},
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     number = {4},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/YJOR_2020_30_4_a0/}
}
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Abubakar Sani Halilu; Mohammed Yusuf Waziri; Ibrahim Yusuf. Efficient Matrix-Free Direction Method With Line Search for Solving Large-Scale System of Nonlinear Equations. Yugoslav journal of operations research, Tome 30 (2020) no. 4, p. 399 . http://geodesic.mathdoc.fr/item/YJOR_2020_30_4_a0/