Spectral CG Algorithm for Solving Fuzzy Nonlinear Equations

Mezher M Abed,Hisham M Khudhur,Ufuk Öztürk

doi:10.52866/ijcsm.2022.01.01.001

Abstract

The nonlinear conjugate gradient method is an effective technique for solving large-scale minimizations problems, and has a wide range of applications in various fields, such as mathematics, chemistry, physics, engineering and medicine. This study presents a novel spectral conjugate gradient algorithm (non-linear conjugate gradient algorithm), which is derived based on the Hisham–Khalil (KH) and Newton algorithms. Based on pure conjugacy condition The importance of this research lies in finding an appropriate method to solve all types of linear and non-linear fuzzy equations because the Buckley and Qu method is ineffective in solving fuzzy equations. Moreover, the conjugate gradient method does not need a Hessian matrix (second partial derivatives of functions) in the solution. The descent property of the proposed method is shown provided that the step size at meets the strong Wolfe conditions. In numerous circumstances, numerical results demonstrate that the proposed technique is more efficient than the Fletcher–Reeves and KH algorithms in solving fuzzy nonlinear equations.

Highlights

IntroductionIterative approaches for solving nonlinear equations such as F(x) = 0 (1)
Iterative approaches for solving nonlinear equations such as F(x) = 0 (1)have received considerable interest in recent years
This study presents a novel spectral conjugate gradient algorithm, which is derived based on the Hisham–Khalil (KH) and Newton algorithms

Summary

Introduction

Iterative approaches for solving nonlinear equations such as F(x) = 0 (1). The concept of fuzzy numbers and the mathematical operations that can be performed on them were first proposed and studied by Zadeh [1]. III- Φy csc(y) + Υy = Ω and IV- Ψy5 − Ω cot(y) = Φ where y, Q, V, L, Θ, K, A, Φ, Υ, Ω, and Ψ are fuzzy numbers. In 2010, Amirah Ramli, Mohd Lazim Abdullah and Mustafa Mamat utilised quasi Newton technique to solve a fuzzy nonlinear equation in [10]. This method is not [Hi], computation of http://journal.esj.edu.iq/index.php/IJCM

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