Open AccessSpectral CG Algorithm for Solving Fuzzy Nonlinear Equations
Author(s) -
Mezher M. Abed,
Ufuk Öztürk,
Hisham M. Khudhur
Publication year - 2022
Publication title -
iraqi journal for computer science and mathematics
Language(s) - English
Resource type - Journals
eISSN - 2958-0544
pISSN - 2788-7421
DOI - 10.52866/ijcsm.2022.01.01.001
Subject(s) - conjugate gradient method , hessian matrix , nonlinear conjugate gradient method , gradient descent , mathematics , conjugacy class , nonlinear system , algorithm , derivation of the conjugate gradient method , gradient method , fuzzy logic , computer science , artificial intelligence , physics , artificial neural network , combinatorics , quantum mechanics
The nonlinear conjugate gradient method is an effective technique for solving large-scaleminimizations 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-linearconjugate gradient algorithm), which is derived based on the Hisham–Khalil (KH) and Newton algorithms. Based onpure conjugacy condition The importance of this research lies in finding an appropriate method to solve all types oflinear 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) inthe solution. The descent property of the proposed method is shown provided that the step size at meets the strongWolfe conditions. In numerous circumstances, numerical results demonstrate that the proposed technique is moreefficient than the Fletcher–Reeves and KH algorithms in solving fuzzy nonlinear equations.