Modified matrix-free methods for solving system of nonlinear equations

Waziri, Mohammed Yusuf; Muhammad, Hadiza Usman; Halilu, Abubakar Sani; Ahmed, Kabiru

doi:10.1080/02331934.2020.1778689

Cited by 26 publications

(8 citation statements)

References 20 publications

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“…In this section, the numerical performance of our method for solving system of nonlinear equations is presented in order to prove the efficiency of the proposed method i.e. HMADD by comparing with (MDF1) [40], (EMD) [27] and (TDS) [29].…”

Section: Numerical Examinationmentioning

confidence: 99%

“…Problem 6 [40]: 2) shows the performance profile of the proposed method based on number of iterations and CPU time (in second) respectively, which were evaluated using the profiles of Dolan and More ′ [11]. We plot the fraction P (τ ) of the problems for which the method is within a factor τ of the best time.…”

Section: Numerical Examinationmentioning

confidence: 99%

“…, where α k ,γ k > 0 are the step size and the acceleration variable, respectively. Waziri [40] recommended a hybrid method for solving (1) by hybridizing the Picard-Mann hybrid process with En -enhance matrix free method and obtained the acceleration parameter as follows:…”

Section: Introductionmentioning

confidence: 99%

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Hybridization of multi-step iterative process with double direction method for solving a system of nonlinear equations and application to motion control

Waziri,

Bala,

Halilu

2023

Preprint

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This article presents a multi-step algorithm for solving a system of nonlinear equations using a double direction approach with application to motion control. In order to offer a useful derivative-free technique, the acceleration parameter is calculated to rougthly approximate the Jacobian matrix. With the aid of an inexact line search approach, the step-length was calculated. In addition, the proposed method is proving to be globally convergent under some appropriate conditions. Numerical experiment for some large-scale benchmark test problems reported in 1 this article shows the efficiency of the suggested methods compared with the current methods in the literature.

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Section: Numerical Examinationmentioning

confidence: 99%

Section: Numerical Examinationmentioning

confidence: 99%

See 1 more Smart Citation

Hybridization of multi-step iterative process with double direction method for solving a system of nonlinear equations and application to motion control

Waziri,

Bala,

Halilu

2023

Preprint

Self Cite

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show abstract

“…The study of such mappings is applied in a variety of scientic areas, including economic and chemical equilibrium systems [37,39,38]. Some iterative methods for solving these problems include Newton method [41], the quasi-Newton methods [4,6,9], the Levenberg-Marquardt methods [42,43], the double direction methods [23,33,29], The double step length methods [17,18,28], and derivative-free methods [34,45,46,44]. But, the famous method used to solve (1) is Newton method that determines the search direction d k by solving the following linear system of equations,…”

Section: Introductionmentioning

confidence: 99%

On efficient matrix-free method via quasi-Newton approach for solving system of nonlinear equations

Wairojjana¹,

Abdullahi²,

Halilu³

et al. 2021

Advances in the Theory of Nonlinear Analysis and Its Application

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In this paper, a matrix-free method for solving large-scale system of nonlinear equations is presented. The method is derived via quasi-Newton approach, where the approximation to the Broyden's update is done by constructing diagonal matrix using acceleration parameter. A fascinating feature of the method is that it is a matrix-free, so is suitable for solving large-scale problems. Furthermore, the convergence analysis of the new method is discussed based on some standard condition. Preliminary numerical results on some test problems show that the method is promising.

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“…Under mild conditions, global convergence of the scheme is proven. For further recent progress on addition methods, we refer the reader to [20,47,48,49,50,40,41,51,21,22] and the references therein.…”

mentioning

confidence: 99%

Modified Dai-Yuan iterative scheme for nonlinear systems and its application

Waziri¹,

Ahmed²,

Halilu³

et al. 2023

NACO

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<p style='text-indent:20px;'>By exploiting the idea employed in the spectral Dai-Yuan method by Xue et al. [IEICE Trans. Inf. Syst. 101 (12)2984-2990 (2018)] and the approach applied in the modified Hager-Zhang scheme for nonsmooth optimization [PLos ONE 11(10): e0164289 (2016)], we develop a Dai-Yuan type iterative scheme for convex constrained nonlinear monotone system. The scheme's algorithm is obtained by combining its search direction with the projection method [Kluwer Academic Publishers, pp. 355-369(1998)]. One of the new scheme's attribute is that it is derivative-free, which makes it ideal for solving non-smooth problems. Furthermore, we demonstrate the method's application in image de-blurring problems by comparing its performance with a recent effective method. By employing mild assumptions, global convergence of the scheme is determined and results of some numerical experiments show the method to be favorable compared to some recent iterative methods.</p>

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Modified matrix-free methods for solving system of nonlinear equations

Cited by 26 publications

References 20 publications

Hybridization of multi-step iterative process with double direction method for solving a system of nonlinear equations and application to motion control

Hybridization of multi-step iterative process with double direction method for solving a system of nonlinear equations and application to motion control

On efficient matrix-free method via quasi-Newton approach for solving system of nonlinear equations

Modified Dai-Yuan iterative scheme for nonlinear systems and its application

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