KMS Of Academy of mathematics and systems sciences, CAS
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 | |
发表期刊 | NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS |
ISSN | 1070-5325 |
卷号 | 24期号:4页码:15 |
摘要 | The 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. |
关键词 | convergence Krylov subspace method matrix splitting iteration preconditioning spatial fractional diffusion equation spectral analysis |
DOI | 10.1002/nla.2093 |
语种 | 英语 |
资助项目 | National Natural Science Foundation[11671393] ; National Natural Science Foundation[11321061] |
WOS研究方向 | Mathematics |
WOS类目 | Mathematics, Applied ; Mathematics |
WOS记录号 | WOS:000405568800004 |
出版者 | WILEY |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | http://ir.amss.ac.cn/handle/2S8OKBNM/26120 |
专题 | 计算数学与科学工程计算研究所 |
通讯作者 | Bai, Zhong-Zhi |
作者单位 | 1.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 |
推荐引用方式 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. |
条目包含的文件 | 条目无相关文件。 |
除非特别说明,本系统中所有内容都受版权保护,并保留所有权利。
修改评论