We propose a variant of the relaxation step used in the most widespread iterative methods (e.g. Jacobi Over-Relaxation, Successive Over-Relaxation) which combines the iteration at the predicted step, namely ( n + 1 ) , with the iteration at step ( n - 1 ) . We provide a theoretical analysis of the proposed algorithm by applying such a delayed relaxation step to a generic (convergent) iterative scheme. We prove that, under proper assumptions, this significantly improves the convergence rate of the initial iterative method. As a relevant example, we apply the proposed algorithm to the solution of the Poisson equation, highlighting the advantages in comparison with classical iterative models. We propose a variant of the relaxation step for iterative solvers.This variant improves the convergence for matrices with real eigenvalues.The proposed scheme profitably applies to elliptic problems.
['Matteo Antuono', 'G. Colicchio']
Delayed Over-Relaxation for iterative methods