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A Non-Krylov Subspace Method for Solving Large and Sparse Linear System of Equations
Peng, Wujian1; Lin, Qun2
AbstractMost current prevalent iterative methods can be classified into the so-called extended Krylov subspace methods, a class of iterative methods which do not fall into this category are also proposed in this paper. Comparing with traditional Krylov subspace methods which always depend on the matrix-vector multiplication with a fixed matrix, the newly introduced methods (the so-called (progressively) accumulated projection methods, or AP (PAP) for short) use a projection matrix which varies in every iteration to form a subspace from which an approximate solution is sought. More importantly an accelerative approach (called APAP) is introduced to improve the convergence of PAP method. Numerical experiments demonstrate some surprisingly improved convergence behavior. Comparison between benchmark extended Krylov subspace methods (Block Jacobi and GMRES) are made and one can also see remarkable advantage of APAP in some examples. APAP is also used to solve systems with extremely ill-conditioned coefficient matrix (the Hilbert matrix) and numerical experiments shows that it can bring very satisfactory results even when the size of system is up to a few thousands.
KeywordIterative method accumulated projection Krylov subspace
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000377119800007
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Document Type期刊论文
Corresponding AuthorPeng, Wujian
Affiliation1.Zhaoqing Univ, Dept Math & Stats Sci, Zhaoqing 526061, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100081, Peoples R China
Recommended Citation
GB/T 7714
Peng, Wujian,Lin, Qun. A Non-Krylov Subspace Method for Solving Large and Sparse Linear System of Equations[J]. NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS,2016,9(2):289-314.
APA Peng, Wujian,&Lin, Qun.(2016).A Non-Krylov Subspace Method for Solving Large and Sparse Linear System of Equations.NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS,9(2),289-314.
MLA Peng, Wujian,et al."A Non-Krylov Subspace Method for Solving Large and Sparse Linear System of Equations".NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS 9.2(2016):289-314.
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