Comparison results on the preconditioned GAOR method for generalized least squares problems

Abstract

Recently, Zhou et al. [Preconditioned GAOR methods for solving weighted linear least squares problems, J. Comput. Appl. Math. 224 (2009), pp. 242–249] have proposed the preconditioned generalized accelerated over relaxation (GAOR) methods for solving generalized least squares problems and studied their convergence rates. In this paper, we propose a new type of preconditioners and study the convergence rates of the new preconditioned GAOR methods for solving generalized least squares problems. Comparison results show that the convergence rates of the new preconditioned GAOR methods are better than those of the preconditioned GAOR methods presented by Zhou et al. whenever these methods are convergent. Lastly, numerical experiments are provided in order to confirm the theoretical results studied in this paper.

Keywords:

• preconditioner
• GAOR method
• preconditioned GAOR method
• generalized least squares problem

1991 AMS Subject Classification::

• 65F10

Acknowledgements

The author thank the anonymous referees and editor-in-chief Abdul Khaliq for their helpful and detailed suggestions for revising this manuscript. This work was supported by the Korea Research Foundation (KRF) grant funded by the Korea government (MEST) (No. 2010-0016538).