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Diagonal and circulant or skew-circulant splitting preconditioners for spatial fractional diffusion equations
Lu, Kang-Ya1,2
2018-09-01
Source PublicationCOMPUTATIONAL & APPLIED MATHEMATICS
ISSN0101-8205
Volume37Issue:4Pages:4196-4218
AbstractWe propose three new preconditioners: diagonal and optimal-circulant splitting preconditioner, diagonal and skew-circulant splitting preconditioner, and diagonal and optimal-skew-circulant splitting preconditioner for solving the diagonal-plus-Toeplitz linear system discretized from the spatial fractional diffusion equations. Theoretical analysis shows that these three preconditioners can make the eigenvalues of the preconditioned matrices be clustered around 1, especially when the grids of the discretizations are refined. These results coincide with the one about the diagonal and circulant splitting preconditioner constructed recently by Bai et al. (Numer Linear Algebra Appl 24:e2093, 2017). Numerical experiments exhibit that the proposed preconditioners can significantly improve the convergence of the Krylov subspace iteration methods like GMRES and BiCGSTAB, and they outperform the diagonal and circulant splitting preconditioner as well.
KeywordCirculant matrix Skew-circulant matrix Preconditioning Spatial fractional diffusion equations
DOI10.1007/s40314-017-0570-6
Language英语
Funding ProjectNational Natural Science Foundation, People's Republic of China[11671393]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000443034900011
PublisherSPRINGER HEIDELBERG
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/31135
Collection中国科学院数学与系统科学研究院
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Sci Engn Comp, Inst Computat Math & Sci Engn Comp, POB 2719, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Lu, Kang-Ya. Diagonal and circulant or skew-circulant splitting preconditioners for spatial fractional diffusion equations[J]. COMPUTATIONAL & APPLIED MATHEMATICS,2018,37(4):4196-4218.
APA Lu, Kang-Ya.(2018).Diagonal and circulant or skew-circulant splitting preconditioners for spatial fractional diffusion equations.COMPUTATIONAL & APPLIED MATHEMATICS,37(4),4196-4218.
MLA Lu, Kang-Ya."Diagonal and circulant or skew-circulant splitting preconditioners for spatial fractional diffusion equations".COMPUTATIONAL & APPLIED MATHEMATICS 37.4(2018):4196-4218.
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