Diagonal and circulant or skew-circulant splitting preconditioners for spatial fractional diffusion equations

doi:10.1007/s40314-017-0570-6

CSpace

	Diagonal and circulant or skew-circulant splitting preconditioners for spatial fractional diffusion equations
	Lu, Kang-Ya 1,2
	2018-09-01
发表期刊	COMPUTATIONAL & APPLIED MATHEMATICS
ISSN	0101-8205
卷号	37 期号:4 页码:4196-4218
摘要	We 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.
关键词	Circulant matrix Skew-circulant matrix Preconditioning Spatial fractional diffusion equations
DOI	10.1007/s40314-017-0570-6
语种	英语
资助项目	National Natural Science Foundation, People's Republic of China[11671393]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000443034900011
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/31135
专题	中国科学院数学与系统科学研究院
通讯作者	Lu, Kang-Ya
作者单位	1.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
推荐引用方式 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.