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A note on the convergence of the two-grid method for Toeplitz systems
Sun, HW; Chan, RH; Chang, QS
1997-07-01
Source PublicationCOMPUTERS & MATHEMATICS WITH APPLICATIONS
ISSN0898-1221
Volume34Issue:1Pages:11-18
AbstractIn this paper, we consider solutions of Toeplitz systems Au = b where the Toeplitz matrices A are generated by nonnegative functions with zeros. Since the matrices A are ill-conditioned, the convergence factor of classical iterative methods, such as the Richardson method, will approach 1 as the size n of the matrices becomes large. In [1,2], convergence of the two-grid method with Richardson method as smoother was proved for band tau matrices and it was conjectured that this convergence result can be carried to Toeplitz systems. In this paper, we show that the two-grid method with Richardson smoother indeed converges for Toeplitz systems that are generated by functions with zeros, provided that the order of the zeros are less than or equal to 2. However, we illustrate by examples that the convergence results of the two-grid method cannot be readily extended to multigrid method for n that are not of the form 2(l) - 1.
Keywordmultigrid method Toeplitz matrices Richardson method damped-Jacobi method
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:A1997XR83800002
PublisherPERGAMON-ELSEVIER SCIENCE LTD
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/29034
Collection中国科学院数学与系统科学研究院
Affiliation1.CHINESE UNIV HONG KONG,DEPT MATH,SHATIN,HONG KONG
2.CHINESE ACAD SCI,INST APPL MATH,BEIJING,PEOPLES R CHINA
Recommended Citation
GB/T 7714
Sun, HW,Chan, RH,Chang, QS. A note on the convergence of the two-grid method for Toeplitz systems[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS,1997,34(1):11-18.
APA Sun, HW,Chan, RH,&Chang, QS.(1997).A note on the convergence of the two-grid method for Toeplitz systems.COMPUTERS & MATHEMATICS WITH APPLICATIONS,34(1),11-18.
MLA Sun, HW,et al."A note on the convergence of the two-grid method for Toeplitz systems".COMPUTERS & MATHEMATICS WITH APPLICATIONS 34.1(1997):11-18.
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