Preconditioned Iterative Methods for Solving Weighted Linear Least Squares Problems

SHEN Hai-long; SHAO Xin-hui; ZHANG Tie

doi:10.3879/j.issn.1000-0887.2012.03.009

Volume 33 Issue 3

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SHEN Hai-long, SHAO Xin-hui, ZHANG Tie. Preconditioned Iterative Methods for Solving Weighted Linear Least Squares Problems[J]. Applied Mathematics and Mechanics, 2012, 33(3): 357-365. doi: 10.3879/j.issn.1000-0887.2012.03.009

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Preconditioned Iterative Methods for Solving Weighted Linear Least Squares Problems

doi: 10.3879/j.issn.1000-0887.2012.03.009

¹College of Sciences, Northeastern University, Shenyang 110004, P.R.China;²College of Information Sciences and Engineering, Northeastern University, Shenyang 110004, P.R.China

Received Date: 2011-10-10
Rev Recd Date: 2011-12-14
Publish Date: 2012-03-15

Abstract

Abstract

The preconditioned iterative methods for solving linear systems based on a class of weighted linear least square problems were proposed, which were the preconditioned generalized accelerated overrelaxation (GAOR) methods. Some convergence and comparison results were obtained. The comparison results show that the convergence rate of the preconditioned iterative methods is indeed better than the rate of the original methods, whenever the original methods are convergent. Furthermore, effectiveness of the new preconditioned methods is shown by numerical experiment.
- preconditioning,
- GAOR method,
- weighted linear least squares problems,
- convergence

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References

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