Theoretical and numerical comparisons of GMRES and WZ-GMRES

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	Theoretical and numerical comparisons of GMRES and WZ-GMRES
	Chen, G. Z. ; Jia, Z. X. ; Chen GZ(陈桂芝)
刊名	http://dx.doi.org/10.1016/j.camwa.2004.04.018
	2004
关键词	KRYLOV SUBSPACE METHODS RESIDUAL METHODS LINEAR-SYSTEMS CONVERGENCE ALGORITHMS ARNOLDI
英文摘要	WZ-GMRES, 'a simpler GMRES' proposed by Walker and Zhou, is mathematically equivalent to the generalized minimal residual method (GMRES) for solving large unsymmetric linear systems of equations. In this paper, relationships are established between two bases of an m-dimensional Krylov subspace K-m (A, r(0)), and the condition number of the transition matrix between two bases is studied. Some relationships are derived between the condition numbers of the small matrices R-G and R-WZ resulting from GMRES and WZ-GMRES, respectively. A detailed analysis shows that generally R-WZ is worse conditioned than R-G, and in particular, R-WZ is definitely ill conditioned when the method is near convergence. Furthermore, numerical behavior of WZ-GMRES is analyzed. It turns out that WZ-GMRES is not numerically equivalent to GMRES when the method is near convergence, and WZ-GMRES is numerically less stable than GMRES and can be numerically unstable. Numerical examples confirm the theoretical results. (C) 2004 Elsevier Ltd. All rights reserved.
语种	英语
内容类型	期刊论文
源URL	[http://dspace.xmu.edu.cn/handle/2288/66882]
专题	数学科学－已发表论文
推荐引用方式 GB/T 7714	Chen, G. Z.,Jia, Z. X.,Chen GZ. Theoretical and numerical comparisons of GMRES and WZ-GMRES[J]. http://dx.doi.org/10.1016/j.camwa.2004.04.018,2004.
APA	Chen, G. Z.,Jia, Z. X.,&陈桂芝.(2004).Theoretical and numerical comparisons of GMRES and WZ-GMRES.http://dx.doi.org/10.1016/j.camwa.2004.04.018.
MLA	Chen, G. Z.,et al."Theoretical and numerical comparisons of GMRES and WZ-GMRES".http://dx.doi.org/10.1016/j.camwa.2004.04.018 (2004).