Some new preconditioned generalized AOR methods for generalized least-squares problems

Abstract

Some new preconditioned GAOR methods for solving generalized least-squares problems and their comparison results are given. Comparison results show that the convergence rates of the new preconditioned GAOR methods are better than those of the preconditioned GAOR methods presented by Shen et al. [Preconditioned iterative methods for solving weighted linear least squares problems, Appl. Math. Mech. – Engl. Ed. 33(3) (2012), pp. 375–384] whenever these methods are convergent. Lastly, numerical experiments are provided to confirm the theoretical results.

Keywords:

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

2000 AMS Subject Classification:

• 65F10

Acknowledgements

The authors are grateful to the editor and referees for their useful and constructive suggestions which made the paper more perfectly. This work was supported by National Natural Science Foundations of China (11361074, 71161020, 71162005) and IRTSTYN.