KMS Of Academy of mathematics and systems sciences, CAS
| Structured preconditioners for nonsingular matrices of block two-by-two structures | |
Bai, ZZ
| |
| 2006 | |
| Source Publication | MATHEMATICS OF COMPUTATION
 |
| ISSN | 0025-5718 |
| Volume | 75Issue:254Pages:791-815 |
| Abstract | For the large sparse block two-by-two real nonsingular matrices, we establish a general framework of practical and efficient structured preconditioners through matrix transformation and matrix approximations. For the specific versions such as modified block Jacobi-type, modified block Gauss-Seidel-type, and modified block unsymmetric (symmetric) Gauss-Seidel-type preconditioners, we precisely describe their concrete expressions and deliberately analyze eigenvalue distributions and positive definiteness of the preconditioned matrices. Also, we show that when these structured preconditioners are employed to precondition the Krylov subspace methods such as GMRES and restarted GMRES, fast and effective iteration solvers can be obtained for the large sparse systems of linear equations with block two-by-two coefficient matrices. In particular, these structured preconditioners can lead to efficient and high-quality preconditioning matrices for some typical matrices from the real-world applications. |
| Keyword | block two-by-two matrix preconditioner modified block relaxation iteration eigenvalue distribution positive definiteness |
| Language | 英语 |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000236723300014 |
| Publisher | AMER MATHEMATICAL SOC |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/2489 |
| Collection | 计算数学与科学工程计算研究所 |
| Corresponding Author | Bai, ZZ |
| Affiliation | Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci Engn Comp, Beijing 100080, Peoples R China |
| Recommended Citation GB/T 7714 | Bai, ZZ. Structured preconditioners for nonsingular matrices of block two-by-two structures[J]. MATHEMATICS OF COMPUTATION,2006,75(254):791-815. |
| APA | Bai, ZZ.(2006).Structured preconditioners for nonsingular matrices of block two-by-two structures.MATHEMATICS OF COMPUTATION,75(254),791-815. |
| MLA | Bai, ZZ."Structured preconditioners for nonsingular matrices of block two-by-two structures".MATHEMATICS OF COMPUTATION 75.254(2006):791-815. |
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