Derivative Free Conjugate Gradient Method via Broyden's Update for solving symmetric systems of nonlinear equations

The applications of mathematics in many areas of computing, scientific and engineering research mostly give rise to a systems of nonlinear equations. Various iterative methods have been developed to solve such equations, this includes Newton method, Quasi-Newton's etc. Over the years, there has...

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Vydané v:Journal of physics. Conference series Ročník 1366; číslo 1; s. 12099 - 12105
Hlavní autori: Dauda, M.K., Mamat, Mustafa, Mohamad, Fatma Susilawati, Magaji, Abubakar S., Waziri, M.Y.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Bristol IOP Publishing 01.11.2019
Predmet:
Applications of mathematics
Computation
Conjugate gradient method
Engineering research
Hessian matrices
Iterative methods
Mathematical analysis
Methods
Nonlinear equations
Nonlinear systems
Optimization
Physics
Quasi Newton methods
Robustness (mathematics)
ISSN:1742-6588, 1742-6596
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Shrnutí:The applications of mathematics in many areas of computing, scientific and engineering research mostly give rise to a systems of nonlinear equations. Various iterative methods have been developed to solve such equations, this includes Newton method, Quasi-Newton's etc. Over the years, there has been significant theoretical study on quasi-Newton methods for solving such systems, but unfortunately the methods suffers setback. To overcome such problems, a Derivative free Method for Solving Symmetric Systems of Nonlinear Equations Using Broyden's Update is presented. The modification is achieved by simply approximating the inverse Hessian matrix Qk+1−1 to QkI with (δk and I represents acceleration parameter and an identity matrix respectively) without computing any derivative. The method uses the symmetric structure of the system sufficiently and the generalized classical Broyden's update method for unconstrained optimization problems. The squared norm merit function is used, both the direction and the line search technique are derivative-free, this attractive feature of the proposed method makes it to have a very low storage requirement thereby solving large scale problems successfully. In an effort to solve nonlinear problems of the form F(x) = 0, 0, x ∈ Rn different initial starting points were used on a set of benchmark test problems, the output is based on number of iterations and CPU time. A comparison between the proposed method and the classical methods were made and found that the proposed method is efficient, robust and outperformed the existing method.
Bibliografia:ObjectType-Article-1
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ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/1366/1/012099