An acceleration of preconditioned generalized accelerated over relaxation methods for systems of linear equations

Abstract

In this paper, a new type of preconditioners are proposed to accelerate the preconditioned generalized accelerated over relaxation methods presented by Zhou et al. [Preconditioned GAOR methods for solving weighted linear least squares problems, J. Comput. Appl. Math. 224 (2009), pp. 242–249] for the linear system of the generalized least-squares problem. The convergence and comparison results are obtained. The comparison results show that the convergence rates of the proposed methods are better than those of the original methods. Finally, numerical experiments are provided to confirm the results obtained in this paper.

Keywords:

• preconditioner
• GAOR method
• generalized least-squares problem
• convergence
• splitting methods

2010 AMS Subject Classifications::

• 65F10
• 65F15
• 65F50

Acknowledgements

The study was financially supported by the National Natural Science Foundation (nos. 11361049 and 71301111).