Convergence of the conjugate gradient method with unbounded operators

On the Rate of Convergence of the Conjugate Gradient Method for Linear Operators in Hilbert Space

New results on the convergence of the conjugate gradient method

This paper is concerned with proving theoretical results related to the convergence of the Conjugate Gradient method for solving positive definite symmetric linear systems. New relations for ratios of the A-norm of the error and the norm of the residual are provided starting from some earlier results of Sadok [13]. These results use the well-known correspondence between the Conjugate Gradient m...

Global convergence of a modified spectral FR conjugate gradient method

A modified spectral PRP conjugate gradient method is presented for solving unconstrained optimization problems. The constructed search direction is proved to be a sufficiently descent direction of the objective function. With an Armijo-type line search to determinate the step length, a new spectral PRP conjugate algorithm is developed. Under some mild conditions, the theory of global convergenc...

Global Convergence of a Modified Liu-storey Conjugate Gradient Method

In this paper, we make a modification to the LS conjugate gradient method and propose a descent LS method. The method can generates sufficient descent direction for the objective function. We prove that the method is globally convergent with an Armijo-type line search. Moreover, under mild conditions, we show that the method is globally convergent if the Armijo line search or the Wolfe line sea...

Deterministic convergence of conjugate gradient method for feedforward neural networks

Conjugate gradient methods have many advantages in real numerical experiments, such as fast convergence and low memory requirements. This paper considers a class of conjugate gradient learning methods for backpropagation (BP) neural networks with three layers. We propose a new learning algorithm for almost cyclic BP neural networks based on PRP conjugate gradient method. We then establish the d...