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Chebyshev polynomial acceleration of SOR method for solving the rank deficient linear systems
Bing Zheng,Liying Duan *
Lanzhou Ｕniversity School of Mathematics and Statistics
*Correspondence author
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Funding: none
Opened online: 2 February 2008
Accepted by: none
Citation: Bing Zheng,Liying Duan.Chebyshev polynomial acceleration of SOR method for solving the rank deficient linear systems[OL]. [ 2 February 2008] http://en.paper.edu.cn/en_releasepaper/content/18572
 
 
Miller and Neumann [V.A. Miller and M. Neumann, Successive overrelaxation methods for solving the rank deficient linear least squares problem, Linear Algebra Appl. 88/89 (1987)] presented the successive overelaxation (SOR) method to solve the linear least squares problem. In this paper, we apply the Chebyshev polynomial to the SOR method and get the C-SOR method. After studying the results of the SOR method, we obtain the interval of the relaxation parameter in which subproper SOR iteration matrix has no complex eigenvalues and the C-SOR method converge. We also give some theorems, which indicate that the C-SOR method has a faster rate of convergence than the SOR method and the corresponding optimum extrapolated method(OE). A numerical example shows that our method is applicable and efficient for soving such rank deficient linear systems.
Keywords:SOR method; Chebyshev polynomial; optimum extrapolated method(the OE method); C-SOR
 
 
 

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