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

In this article, we proposed two Conjugate Gradient (CG) parameters using the modified Dai–Liao condition and descent three-term CG search direction. Both are incorporated with projection technique for solving large-scale monotone nonlinear equations. Using Lipschitz assumptions, global convergence of methods has been proved. Finally, numerical results provided to illustrate robustness methods.

This paper presents an iterative algorithm for solving intuitionistic fuzzy nonlinear equations (IFNEs). The proposed method is based on the classical conjugate gradient (CG) search direction. An interesting feature of new that it considers problems special triangular number. For this purpose, quantities are transformed into membership and non-membership parametric forms, a line procedure emplo...

Abstract A Polak–Ribière–Polyak (PRP) algorithm is one of the oldest and popular conjugate gradient algorithms for solving nonlinear unconstrained optimization problems. In this paper, we present a q -variant PRP ( -PRP) method which both sufficient conjugacy conditions are satisfied at every iteration. The proposed convergent globally with standard Wolfe strong conditions. numerical results sh...

A modi ed backpropagation learning algorithm for training arti cial neural networks using de ecting gradient technique, which may be considered as a special case of the conjugate gradient methods, is proposed. Parallel tangent(Partan) gradient is used as an alternative for momentum term to accelerate the convergence. Partan gradient consists of two phases namely, climbing through gradient and a...

In our papers [Inverse Problems, 15, 309-327,1999] and [Numer. Math., 88, 347-365, 2001] we proposed algorithm REGINN being an inexact Newton iteration for the stable solution of nonlinear ill-posed problems. REGINN consists of two components: the outer iteration, which is a Newton iteration stopped by the discrepancy principle, and an inner iteration, which computes the Newton correction by so...

An important variation of preconditioned conjugate gradient algorithms is inexact precon-ditioner implemented with inner-outer iterations 5], where the preconditioner is solved by an inner iteration to a prescribed precision. In this paper, we formulate an inexact preconditioned conjugate gradient algorithm for a symmetric positive deenite system and analyze its convergence property. We establi...

in this paper, the conjugate gradient method coupled with adjoint problem is used in order to solve the inverse heat conduction problem and estimation of the time- dependent heat flux using the temperature distribution at a point in a three layer system with none homogeneous boundary conditions. also, the effect of noisy data on final solution is studied. for solving this problem the general co...