Preconditioned conjugate gradient method and generalized successive over relaxation method for the weighted least squares problems

Abstract

In this paper, the connection between the generalized successive over relaxation (GSOR) method and the preconditioned conjugate gradient (PCG) method for the normal equations is investigated. It is shown that the PCG method is at least as fast as the GSOR method. Numerical examples demonstrates that the PCG method is much faster than the GSOR method.

^†Email: [email protected]

^‡Email: [email protected]

Keywords:

• Weighted least squares problem
• Generalized successive overrelaxation method
• Preconditioned conjugate gradient method

Acknowledgments

The authors would like to thank Prof. D. J. Evans and the referee for their useful comments and providing them with the preprint [12]. The paper was supported by the National Natural Science Foundation under grant 19901006 and 10171021.

Notes

^†Email: [email protected]

^‡Email: [email protected]