KMS Of Academy of mathematics and systems sciences, CAS
A class of nested iteration schemes for linear systems with a coefficient matrix with a dominant positive definite symmetric part | |
Axelsson, O; Bai, ZZ; Qiu, SX | |
2004-04-01 | |
Source Publication | NUMERICAL ALGORITHMS |
ISSN | 1017-1398 |
Volume | 35Issue:2-4Pages:351-372 |
Abstract | We present a class of nested iteration schemes for solving large sparse systems of linear equations with a coefficient matrix with a dominant symmetric positive definite part. These new schemes are actually inner/outer iterations, which employ the classical conjugate gradient method as inner iteration to approximate each outer iterate, while each outer iteration is induced by a convergent and symmetric positive definite splitting of the coefficient matrix. Convergence properties of the new schemes are studied in depth, possible choices of the inner iteration steps are discussed in detail, and numerical examples from the finite-difference discretization of a second-order partial differential equation are used to further examine the effectiveness and robustness of the new schemes over GMRES and its preconditioned variant. Also, we show that the new schemes are, at least, comparable to the variable-step generalized conjugate gradient method and its preconditioned variant. |
Keyword | system of linear equations inner/outer iteration conjugate gradient method Krylov subspace iterations incomplete factorization relaxation iteration convergence theory |
Language | 英语 |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied |
WOS ID | WOS:000220453200014 |
Publisher | KLUWER ACADEMIC PUBL |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/1003 |
Collection | 计算数学与科学工程计算研究所 |
Corresponding Author | Axelsson, O |
Affiliation | 1.Catholic Univ Nijmegen, Fac Math & Informat, NL-6525 ED Nijmegen, Netherlands 2.Chinese Acad Sci, State Key Lab Sci Engn Comp, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100080, Peoples R China |
Recommended Citation GB/T 7714 | Axelsson, O,Bai, ZZ,Qiu, SX. A class of nested iteration schemes for linear systems with a coefficient matrix with a dominant positive definite symmetric part[J]. NUMERICAL ALGORITHMS,2004,35(2-4):351-372. |
APA | Axelsson, O,Bai, ZZ,&Qiu, SX.(2004).A class of nested iteration schemes for linear systems with a coefficient matrix with a dominant positive definite symmetric part.NUMERICAL ALGORITHMS,35(2-4),351-372. |
MLA | Axelsson, O,et al."A class of nested iteration schemes for linear systems with a coefficient matrix with a dominant positive definite symmetric part".NUMERICAL ALGORITHMS 35.2-4(2004):351-372. |
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