Inexact Cg-Method via Sr1 Update for Solving Systems of Nonlinear Equations

Dauda, Mohammed; Mamat, Mustafa; Waziri, Mohammed Yusuf; Ahmad, Fadhila; Mohamad, Fatma Susilawati

doi:10.17654/ms100111787

Cited by 8 publications

(11 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The computational experiment is based on the number of iterations and CPU time. To ascertain the global convergence of the proposed method, the benchmarks problems in [21,22] was used with two different ISP, and the output of the performance of the methods was based on the performance profile presented by Dolan and More [24]. The performance profile : → [0,1] is defined as follows: Let and be the set of problems and set of solvers respectively.…”

Section: Numerical Resultsmentioning

confidence: 99%

Hybrid conjugate gradient parameter for solving symmetric systems of nonlinear equations

Dauda

Mamat

Mohamed

et al. 2019

IJEECS

Self Cite

View full text Add to dashboard Cite

Mathematical models from recent research are mostly nonlinear equations in nature. Numerical solutions to such systems are widely needed and applied in those areas of mathematics. Although, in recent years, this field received serious attentions and new approach were discovered, but yet the efficiency of the previous versions suffers setback. This article gives a new hybrid conjugate gradient parameter, the method is derivative-free and analyzed with an effective inexact line search in a given conditions. Theoretical proofs show that the proposed method retains the sufficient descent and global convergence properties of the original CG methods. The proposed method is tested on a set of test functions, then compared to the two previous classical CG-parameter that resulted the given method, and its performance is given based on number of iterations and CPU time. The numerical results show that the new proposed method is efficient and effective amongst all the methods tested. The graphical representation of the result justify our findings. The computational result indicates that the new hybrid conjugate gradient parameter is suitable and capable for solving symmetric systems of nonlinear equations.

show abstract

Section: Numerical Resultsmentioning

confidence: 99%

Hybrid conjugate gradient parameter for solving symmetric systems of nonlinear equations

Dauda

Mamat

Mohamed

et al. 2019

IJEECS

Self Cite

View full text Add to dashboard Cite

show abstract

“…PROBLEM 1 [3] ( ) = ( ) 2 + ( − − 1); = 1,2,3, ⋯ , . 0 = (0.9,0.9,0.9, ⋯ ,0.9) and 0 = (0.7,0.7,0.7, ⋯ ,0.7)…”

Section: List Of Benchmark Test Problem Usedmentioning

confidence: 99%

“…( ) = 0, ∈ ; (Eq 1) where : → is continuously differentiable. Newton and quasi-Newton methods are the most widely used methods to solve such problems because they have very attractive convergence properties and practical application (see [1,2,3,4]). However, they are not usually suitable for large-scale nonlinear systems of equations because they require Jacobian matrix, or an approximation to it, at every iteration while solving optimization problems.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An Alternative Modified Conjugate Gradient Coefficient for Solving Nonlinear System of Equations

Dauda¹,

Usman²,

Ubale³

et al. 2019

Opn J Sci & Tech

View full text Add to dashboard Cite

In mathematical term, the method of solving models and finding the best alternatives is known as optimization. Conjugate gradient (CG) method is an evolution of computational method in solving optimization problems. In this article, an alternative modified conjugate gradient coefficient for solving large-scale nonlinear system of equations is presented. The method is an improved version of the Rivaie et el conjugate gradient method for unconstrained optimization problems. The new CG is tested on a set of test functions under exact line search. The approach is easy to implement due to its derivative-free nature and has been proven to be effective in solving real-life application. Under some mild assumptions, the global convergence of the proposed method is established. The new CG coefficient also retains the sufficient descent condition. The performance of the new method is compared to the well-known previous PRP CG methods based on number of iterations and CPU time. Numerical results using some benchmark problems show that the proposed method is promising and has the best efficiency amongst all the methods tested.

show abstract

“…Furthermore, the search direction is generally required to satisfy the descent condition ∇ ( ) < 0. The derivative-free direction can be obtained in several ways [4,5,7,9,12]. An iterative method that generates a sequence { } satisfying (3) or (5) is called a norm descent method.…”

Section: Introductionmentioning

confidence: 99%

A Derivative-Free Decent Method Via Acceleration Parameter for Solving Systems of Nonlinear Equations

Halilu¹,

Dauda²,

Waziri³

et al. 2019

Opn J Sci & Tech

View full text Add to dashboard Cite

An algorithm for solving large-scale systems of nonlinear equations based on the transformation of the Newton method with the line search into a derivative-free descent method is introduced. Main idea used in the algorithm construction is to approximate the Jacobian by an appropriate diagonal matrix. Furthermore, the step length is calculated using inexact line search procedure. Under appropriate conditions, the proposed method is proved to be globally convergent under mild conditions. The numerical results presented show the efficiency of the proposed method.

show abstract

Inexact Cg-Method via Sr1 Update for Solving Systems of Nonlinear Equations

Cited by 8 publications

References 0 publications

Hybrid conjugate gradient parameter for solving symmetric systems of nonlinear equations

Hybrid conjugate gradient parameter for solving symmetric systems of nonlinear equations

An Alternative Modified Conjugate Gradient Coefficient for Solving Nonlinear System of Equations

A Derivative-Free Decent Method Via Acceleration Parameter for Solving Systems of Nonlinear Equations

Contact Info

Product

Resources

About