A Delayed Weighted Gradient Method for Strictly Convex Quadratic Minimization

Autor: Harry Fernando Oviedo Leon
This paper develops an accelerated version of the steepest descent method by a two-step iteration. The new algorithm uses information with delay to de ne the iterations. Speci cally, in the rst step, a prediction of the new test point is calculated by using the gradient method with the exact minimal gradient steplength and then, a correction is computed by a weighted sum between the prediction and the iterate predecessor to the previous point. A convergence result is studied. Some numerical experiments are performed, in order to compare the eciency and e ectiveness of the proposed method with similar methods existing in the literature. The numerical results show that the new algorithm, presents a competitive performance to the classical conjugate gradient method, which makes this procedure a good alternative to solve large-scale problems.