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Structured preconditioners for nonsingular matrices of block two-by-two structures
Bai, ZZ
AbstractFor 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.
Keywordblock two-by-two matrix preconditioner modified block relaxation iteration eigenvalue distribution positive definiteness
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000236723300014
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Document Type期刊论文
Corresponding AuthorBai, ZZ
AffiliationChinese 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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