An improved three-term derivative-free method for solving nonlinear equations

Abubakar, Auwal Bala

doi:10.1007/s40314-018-0712-5

Cited by 37 publications

(32 citation statements)

References 33 publications

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“…In this section, we give the details of the proposed method. We start by briefly reviewing the work of Abubakar and Kumam [21] and that of Liu and Li [22]. Most recently, Abubakar and Kumam [21] proposed the direction…”

Section: Algorithmmentioning

confidence: 99%

“…The global convergence of this method was also established using the line search (4). For other conjugate gradient-based projection methods, the reader is referred to [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, following the work of Abubakar and Kumam [21], Hu and Wei [11] and that of Liu and Li [22], we propose a self adaptive spectral conjugate gradient-based projection method for solving systems of nonlinear monotone Eq. (1).…”

Section: Introductionmentioning

confidence: 99%

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Self adaptive spectral conjugate gradient method for solving nonlinear monotone equations

Koorapetse

Kaelo

2020

J Egypt Math Soc

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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 F T k d k ≤ −c F k 2 , 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.

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Section: Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Self adaptive spectral conjugate gradient method for solving nonlinear monotone equations

Koorapetse

Kaelo

2020

J Egypt Math Soc

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“…One of the famous method for solving is the Newton method, which generates a sequence { x k } using the formula

x_{k + 1} = x_{k} - J {(x_{k})}^{- 1} F (x_{k}), \forall k = 0, 1, 2, … .

The Newton method has a very good convergence property but have some shortcomings such as Jacobian computation per iteration, which is costly. Other methods for solving are quasi Newton methods, spectral gradient methods, conjugate gradient methods, etc . For simplicity, we denote F k = F ( x k ) and J k = J ( x k ).…”

Section: Introductionmentioning

confidence: 99%

“…Other methods for solving (1) are quasi Newton methods, spectral gradient methods, conjugate gradient methods, etc. [2][3][4][5][6][7][8][9] For simplicity, we denote F k = F(x k ) and J k = J(x k ). Methods for solving symmetric nonlinear problem (1) has been proposed by many authors.…”

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confidence: 99%

An inexact conjugate gradient method for symmetric nonlinear equations

Abubakar

Awwal

2019

Comp and Math Methods

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In this article, we present a conjugate gradient method for large‐scale nonlinear equations with symmetric Jacobian. The method is a modification of the descent Dai‐Liao conjugate gradient method for unconstrained optimization problem proposed by Kafaki and Gambari. Under some assumptions, which include symmetric property of the Jacobian, we establish the global convergence of the proposed method and, finally, some numerical results to show its efficiency.

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Two derivative‐free algorithms for constrained nonlinear monotone equations

Abubakar

Mohammad

Waziri

2021

Comp and Math Methods

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We propose two positive parameters based on the choice of Birgin and Martínez search direction. Using the two classical choices of the Barzilai-Borwein parameters, two positive parameters were derived by minimizing the distance between the relative matrix corresponding to the propose search direction and the scaled memory-less Broyden-Fletcher-Goldfarb-Shanno (BFGS) matrix in the Frobenius norm. Moreover, the resulting direction is descent independent of any line search condition. We established the global convergence of the proposed algorithm under some appropriate assumptions. In addition, numerical experiments on some benchmark test problems are reported in order to show the efficiency of the proposed algorithm.

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An improved three-term derivative-free method for solving nonlinear equations

Cited by 37 publications

References 33 publications

Self adaptive spectral conjugate gradient method for solving nonlinear monotone equations

Self adaptive spectral conjugate gradient method for solving nonlinear monotone equations

An inexact conjugate gradient method for symmetric nonlinear equations

Two derivative‐free algorithms for constrained nonlinear monotone equations

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