Modification of the new conjugate gradient algorithm to solve nonlinear fuzzy equations

Abstract

The conjugate gradient approach is a powerful tool that is used in a variety of areas to solve problems involving large-scale reduction. In this paper, we propose a new parameter in nonlinear conjugate gradient algorithms to solve nonlinear fuzzy equations based on Polak and Ribiere (PRP) method, where we prove the descent and global convergence properties of the proposed algorithm. In terms of numerical results, the new method has been compared with the methods of Fletcher (CD), Fletcher and Reeves (FR), and Polak and Ribiere (PRP). The proposed algorithm has outperformed the rest of the algorithms in the number of iterations and in finding the best value for the function and the best value for the variables.