Shadow block iteration for solving linear systems obtained from wavelet transforms

doi:10.1016/j.acha.2005.01.004

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	Shadow block iteration for solving linear systems obtained from wavelet transforms
	Lu, Y ; Shen, LX ; Xu, YS
	2005-11-01
发表期刊	APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
ISSN	1063-5203
卷号	19 期号:3 页码:359-385
摘要	Matrices resulting from wavelet transforms have a special "shadow" block structure, that is, their small upper left blocks contain their lower frequency information. Numerical solutions of linear systems with such matrices require special care. We propose shadow block iterative methods for solving linear systems of this type. Convergence analysis for these algorithms are presented. We apply the algorithms to three applications: linear systems arising in the classical regularization with a single parameter for the signal de-blurring problem, multilevel regularization with multiple parameters for the same problem and the Galerkin method of solving differential equations. We also demonstrate the efficiency of these algorithms by numerical examples ill these applications. (c) 2005 Elsevier Inc. All rights reserved.
关键词	wavelets block iterations regularization deblurring
DOI	10.1016/j.acha.2005.01.004
语种	英语
WOS研究方向	Mathematics ; Physics
WOS类目	Mathematics, Applied ; Physics, Mathematical
WOS记录号	WOS:000234001200005
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/1292
专题	中国科学院数学与系统科学研究院
通讯作者	Shen, LX
作者单位	1.Western Michigan Univ, Dept Math, Kalamazoo, MI 49008 USA 2.Acad Sinica, Acad Math & Syst Sci, Beijing 100080, Peoples R China 3.Syracuse Univ, Dept Math, Syracuse, NY 13244 USA 4.Chinese Acad Sci, Inst Math, Acad Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Lu, Y,Shen, LX,Xu, YS. Shadow block iteration for solving linear systems obtained from wavelet transforms[J]. APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS,2005,19(3):359-385.
APA	Lu, Y,Shen, LX,&Xu, YS.(2005).Shadow block iteration for solving linear systems obtained from wavelet transforms.APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS,19(3),359-385.
MLA	Lu, Y,et al."Shadow block iteration for solving linear systems obtained from wavelet transforms".APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS 19.3(2005):359-385.