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Diagonal and Toeplitz splitting iteration methods for diagonal-plus-Toeplitz linear systems from spatial fractional diffusion equations
Bai, Zhong-Zhi1,2; Lu, Kang-Ya1,2; Pan, Jian-Yu3
2017-08-01
Source PublicationNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
ISSN1070-5325
Volume24Issue:4Pages:15
AbstractThe finite difference discretization of the spatial fractional diffusion equations gives discretized linear systems whose coefficient matrices have a diagonal-plus-Toeplitz structure. For solving these diagonal-plus-Toeplitz linear systems, we construct a class of diagonal and Toeplitz splitting iteration methods and establish its unconditional convergence theory. In particular, we derive a sharp upper bound about its asymptotic convergence rate and deduct the optimal value of its iteration parameter. The diagonal and Toeplitz splitting iteration method naturally leads to a diagonal and circulant splitting preconditioner. Analysis shows that the eigenvalues of the corresponding preconditioned matrix are clustered around 1, especially when the discretization step-size h is small. Numerical results exhibit that the diagonal and circulant splitting preconditioner can significantly improve the convergence properties of GMRES and BiCGSTAB, and these preconditioned Krylov subspace iteration methods outperform the conjugate gradient method preconditioned by the approximate inverse circulant-plus-diagonal preconditioner proposed recently by Ng and Pan (M.K. Ng and J.-Y. Pan, SIAM J. Sci. Comput. 2010;32:1442-1464). Moreover, unlike this preconditioned conjugate gradient method, the preconditioned GMRES and BiCGSTAB methods show h-independent convergence behavior even for the spatial fractional diffusion equations of discontinuous or big-jump coefficients.
Keywordconvergence Krylov subspace method matrix splitting iteration preconditioning spatial fractional diffusion equation spectral analysis
DOI10.1002/nla.2093
Language英语
Funding ProjectNational Natural Science Foundation[11671393] ; National Natural Science Foundation[11321061]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000405568800004
PublisherWILEY
Citation statistics
Cited Times:5[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/26120
Collection计算数学与科学工程计算研究所
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci Engn Comp, POB 2719, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
3.East China Normal Univ, Dept Math, Shanghai 200241, Peoples R China
Recommended Citation
GB/T 7714
Bai, Zhong-Zhi,Lu, Kang-Ya,Pan, Jian-Yu. Diagonal and Toeplitz splitting iteration methods for diagonal-plus-Toeplitz linear systems from spatial fractional diffusion equations[J]. NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS,2017,24(4):15.
APA Bai, Zhong-Zhi,Lu, Kang-Ya,&Pan, Jian-Yu.(2017).Diagonal and Toeplitz splitting iteration methods for diagonal-plus-Toeplitz linear systems from spatial fractional diffusion equations.NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS,24(4),15.
MLA Bai, Zhong-Zhi,et al."Diagonal and Toeplitz splitting iteration methods for diagonal-plus-Toeplitz linear systems from spatial fractional diffusion equations".NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS 24.4(2017):15.
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