Chebyshev polynomial acceleration for block SOR methods for solving the rank-deficient least-squares problem

Abstract

In this article, we give the acceleration of the block successive overrelaxation (SOR) method for solving the rank-deficient least-squares problem. Santos and Silva proposed the two-block SOR method and the three-block SOR method. Here, we consider the acceleration of the two-block SOR method and the three-block SOR method using the Chebyshev polynomial and derive what we term the C-2-block SOR method and the C-3-block SOR method. The advantage of our methods is that we can get good results with very small iteration number. The comparison between the C-2-block method and the C-3-block method is presented. Finally, numerical examples are given.

Keywords:

• two-block SOR method
• three-block SOR method
• Chebyshev polynomial
• C-2-block SOR method
• C-3-block SOR method

2000 AMS Subject Classifications :

• 65B99
• 65F10
• 65F20

Acknowledgements

Bing Zheng was supported by the Fundamental Research Fund for Physics and Mathematics of Lanzhou University and Gansu Project of Science and Technology (096RJZA049), People's Republic of China.KeWangwas supported by Innovation Fund of Shanghai University (No. A.10-0101-08-402), Special Fund for the Selective Cultivation of ExcellentYouth University Teacher in Shanghai (No. B.37-0101-08-005) and Shanghai Leading Academic Discipline Project (J50101), People's Republic of China.

Additional information

Notes on contributors

Liying Duan

Current address: Qinghuangdao Branch, Beijing Institute of Technology, Qinghuangdao 066100, China