CSpace  > 计算数学与科学工程计算研究所
Modified incomplete orthogonal factorization methods using Givens rotations
Bai, Zhong-Zhi; Yin, Jun-Feng
Source PublicationCOMPUTING
AbstractWe present a class of new preconditioners based on the incomplete Givens orthogonalization (IGO) methods for solving large sparse systems of linear equations. In the new methods, instead of dropping entries and accepting fill-ins according to the magnitudes of values and the sparsity patterns, we adopt a diagonal compensation strategy, in which the dropped entries are re-used by adding to the main diagonal entries of the same rows of the incomplete upper-triangular factors, possibly after suitable relaxation treatments, so that certain constraints on the preconditioning matrices are further satisfied. This strategy can make the computed preconditioning matrices possess certain desired properties, e.g., having the same weighted row sums as the target matrices. Theoretical analysis shows that these modified incomplete Givens orthogonalization (MIGO) methods can preserve certain useful properties of the original matrix, and numerical results are used to verify the stability, the accuracy, and the efficiency of the MIGO methods employed to precondition the Krylov subspace iteration methods such as GMRES. Both theoretical and numerical studies show that the MIGO methods may have the potential to present high-quality preconditioners for large sparse nonsymmetric matrices.
KeywordPreconditioner Givens rotation Incomplete orthogonal factorization Nonsymmetric matrix
Funding ProjectNational Basic Research Program[2005CB321702] ; China Outstanding Young Scientist Foundation[10525102] ; National Natural Science Foundation[10471146]
WOS Research AreaComputer Science
WOS SubjectComputer Science, Theory & Methods
WOS IDWOS:000269926700004
Citation statistics
Document Type期刊论文
Corresponding AuthorBai, Zhong-Zhi
AffiliationChinese Acad Sci, State Key Lab Sci Engn Comp, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Bai, Zhong-Zhi,Yin, Jun-Feng. Modified incomplete orthogonal factorization methods using Givens rotations[J]. COMPUTING,2009,86(1):53-69.
APA Bai, Zhong-Zhi,&Yin, Jun-Feng.(2009).Modified incomplete orthogonal factorization methods using Givens rotations.COMPUTING,86(1),53-69.
MLA Bai, Zhong-Zhi,et al."Modified incomplete orthogonal factorization methods using Givens rotations".COMPUTING 86.1(2009):53-69.
Files in This Item:
There are no files associated with this item.
Related Services
Recommend this item
Usage statistics
Export to Endnote
Google Scholar
Similar articles in Google Scholar
[Bai, Zhong-Zhi]'s Articles
[Yin, Jun-Feng]'s Articles
Baidu academic
Similar articles in Baidu academic
[Bai, Zhong-Zhi]'s Articles
[Yin, Jun-Feng]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[Bai, Zhong-Zhi]'s Articles
[Yin, Jun-Feng]'s Articles
Terms of Use
No data!
Social Bookmark/Share
All comments (0)
No comment.

Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.