NEW PRECONDITIONED GAOR METHODS FOR BLOCK LINEAR SYSTEM ARISING FROM WEIGHTED LINEAR LEAST SQUARES PROBLEMS

Shu-Xin Miao; Li Wang; Guang-Bin Wang

doi:10.11948/20190164

2021 Volume 11 Issue 2

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Shu-Xin Miao, Li Wang, Guang-Bin Wang. NEW PRECONDITIONED GAOR METHODS FOR BLOCK LINEAR SYSTEM ARISING FROM WEIGHTED LINEAR LEAST SQUARES PROBLEMS[J]. Journal of Applied Analysis & Computation, 2021, 11(2): 656-673. doi: 10.11948/20190164

Citation:

Shu-Xin Miao, Li Wang, Guang-Bin Wang. NEW PRECONDITIONED GAOR METHODS FOR BLOCK LINEAR SYSTEM ARISING FROM WEIGHTED LINEAR LEAST SQUARES PROBLEMS[J]. Journal of Applied Analysis & Computation, 2021, 11(2): 656-673. doi: 10.11948/20190164

NEW PRECONDITIONED GAOR METHODS FOR BLOCK LINEAR SYSTEM ARISING FROM WEIGHTED LINEAR LEAST SQUARES PROBLEMS

1.
College of Mathematics and Statistics, Northwest Normal University, 730070, Lanzhou, China
2.
Department of Mathematics, Qingdao Agricultural University, 266109, Qingdao, China

Corresponding author: Email: wguangbin750828@sina.com (G. Wang)
Fund Project: The authors were supported by the Natural Science Foundation of China (No. 11861059), Natural Science Foundation of Northwest Normal University (No. NWNU-LKQN-17-5) and the Science and Technology Program of Shandong Colleges (J16LI04)

Abstract

Abstract

In this paper, new preconditioned GAOR methods are proposed for solving a class of $ 2 \times 2 $ block structure linear systems arising from the weighted linear least squares problems. Comparison theorems are derived. Comparison results show that the convergence rates of the new preconditioned GAOR methods are better than those of the preconditioned GAOR methods in the previous literatures whenever these methods are convergent. A numerical example is given to confirm our theoretical results.
- Preconditioner /
- GAOR method /
- preconditioned GAOR method /
- weighted linear least squares problem /
- comparison theorem
MSC: 65F10, 65F50

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References

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