Iranian Journal of Optimization
,
Issue5,Year,
Spring
2020
In this paper, we develop a new eighth-order method for simple roots of non- linear equations via weight function and interpolation methods. The method requires only three(3) function evaluation and a derivative evaluation with 81/4 ≈ 1.682 efficiency index . Nume More
In this paper, we develop a new eighth-order method for simple roots of non- linear equations via weight function and interpolation methods. The method requires only three(3) function evaluation and a derivative evaluation with 81/4 ≈ 1.682 efficiency index . Numerical comparison between the proposed method with some other methods were presented, which shows that our method is promising .
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Iranian Journal of Optimization
,
Issue2,Year,
Winter
2020
There exist large varieties of conjugate gradient algorithms. In order to take advantage of the attractive features of Liu and Storey (LS) and Conjugate Descent (CD) conjugate gradient methods, we suggest hybridization of these methods in which the parameter is computed More
There exist large varieties of conjugate gradient algorithms. In order to take advantage of the attractive features of Liu and Storey (LS) and Conjugate Descent (CD) conjugate gradient methods, we suggest hybridization of these methods in which the parameter is computed as a convex combination of and respectively which the conjugate gradient (update) parameter was obtained from Secant equation. The algorithm generates descent direction and when the iterate jam, the direction satisfy sufficient descent condition. We report numerical results demonstrating the efficiency of our method. The hybrid computational scheme outperform or comparable with known conjugate gradient algorithms. We also show that our method converge globally using strong Wolfe condition.
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Iranian Journal of Optimization
,
Issue1,Year,
Winter
2022
In this article, the improvement of the numerical performance of the iterative scheme presented by Halilu and Waziri in [5] is considered. This is made possible by hybridizing it with Picard-Mann hybrid iterative process. In addition, the step length is calculated using More
In this article, the improvement of the numerical performance of the iterative scheme presented by Halilu and Waziri in [5] is considered. This is made possible by hybridizing it with Picard-Mann hybrid iterative process. In addition, the step length is calculated using the inexact line search technique. Under the preliminary conditions, the proposed method's global convergence is established. The numerical experiment shown in this paper depicts the efficiency of the proposed method, which improved the results than the double direction method [5], existing in the literature.
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International Journal of Mathematical Modeling & Computations
,
Issue2,Year,
Spring
2017
Nonlinear conjugate gradient method is well known in solving large-scale unconstrained optimization problems due to it’s low storage requirement and simple to implement. Research activities on it’s application to handle higher dimensional systems of nonlinea More
Nonlinear conjugate gradient method is well known in solving large-scale unconstrained optimization problems due to it’s low storage requirement and simple to implement. Research activities on it’s application to handle higher dimensional systems of nonlinear equations are just beginning. This paper presents a Threeterm Conjugate Gradient algorithm for solving Large-Scale systems of nonlinear equations by incoporating the hyperplane projection and Powel restart approach. We prove the global convergence of the proposed method with a derivative free line search under suitable assumtions. the numerical results are presented which show that the proposed method is promising.
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International Journal of Mathematical Modeling & Computations
,
Issue4,Year,
Summer
2019
In this paper, we proposed a three-point iterative method for finding the simple roots of non- linear equations via mid-point and interpolation approach. The method requires one evaluation of the derivative and three(3) functions evaluation with efficiency index of 81/4 More
In this paper, we proposed a three-point iterative method for finding the simple roots of non- linear equations via mid-point and interpolation approach. The method requires one evaluation of the derivative and three(3) functions evaluation with efficiency index of 81/4 ≈ 1.682. Numerical results reported here, between the proposed method with some other existing methods shows that our method is promising.
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