Preconditioned GAOR methods for solving weighted linear least squares problems

Authors:
Xiaoxia Zhou;Yongzhong Song;Li Wang;Qingsheng Liu
Affiliations:
Institute of Mathematics, Nanjing Normal University, Nanjing 210097, People's Republic of China;Institute of Mathematics, Nanjing Normal University, Nanjing 210097, People's Republic of China;Institute of Mathematics, Nanjing Normal University, Nanjing 210097, People's Republic of China;Institute of Mathematics, Nanjing Normal University, Nanjing 210097, People's Republic of China
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

Citing 3
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Abstract

In this paper, we present the preconditioned generalized accelerated overrelaxation (GAOR) method for solving linear systems based on a class of weighted linear least square problems. Two kinds of preconditioning are proposed, and each one contains three preconditioners. We compare the spectral radii of the iteration matrices of the preconditioned and the original methods. The comparison results show that the convergence rate of the preconditioned GAOR methods is indeed better than the rate of the original method, whenever the original method is convergent. Finally, a numerical example is presented in order to confirm these theoretical results.