A New Cyclic Gradient Method Adapted to Large-Scale Linear Systems

Abstract

This paper proposes a new gradient method to solve the large-scale problems. Theoretical analysis shows that the new method has finite termination property for two dimensions and converges R-linearly for any dimensions. Experimental results illustrate first the issue of parallel implementation. Then, the solution of a large-scale problem shows that the new method is better than the others, even competitive with the conjugate gradient method.

On Extensions of Limited Memory Steepest Descent Method

“…A theorem provided in [6] could prove its convergence when α n follows the framework of gradient method with retards. It was recently shown in [16,20] that cyclic formulation may accelerate the iteration process both in terms of sequential and parallel computation. The main steps based on this strategy can be stated as follows:…”