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 Modulus-based iterative methods for constrained Tikhonov regularization Bai, Zhong-Zhi1; Buccini, Alessandro2; Hayami, Ken3,4; Reichel, Lothar5; Yin, Jun-Feng6; Zheng, Ning3,4 2017-08-01 Source Publication JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS ISSN 0377-0427 Volume 319Pages:1-13 Abstract Tikhonov regularization is one of the most popular methods for the solution of linear discrete ill-posed problems. In many applications the desired solution is known to lie in the nonnegative cone. It is then natural to require that the approXimate solution determined by Tikhonov regularization also lies in this cone. The present paper describes two iterative methods, that employ modulus-based iterative methods, to compute approximate solutions in the nonnegative cone of large-scale Tikhonov regularization problems. The first method considered consists of two steps: first the given linear discrete ill-posed problem is reduced to a small problem by a Krylov subspace method, and then the reduced Tikhonov regularization problems so obtained is solved. The second method described explores the structure of certain image restoration problems. Computed examples illustrate the performances of these methods. (C) 2016 Elsevier B.V. All rights reserved. Keyword Discrete ill-posed problem Regularization method Constrained minimization DOI 10.1016/j.cam.2016.12.023 Language 英语 Funding Project National Natural Science Foundation, P.R. China[11671393] ; MIUR-PRIN[2012MTE38N] ; GNCS of INdAM Project : New aspects of imaging regularization WOS Research Area Mathematics WOS Subject Mathematics, Applied WOS ID WOS:000397362900001 Publisher ELSEVIER SCIENCE BV Citation statistics Document Type 期刊论文 Identifier http://ir.amss.ac.cn/handle/2S8OKBNM/25207 Collection 计算数学与科学工程计算研究所 Corresponding Author Buccini, Alessandro Affiliation 1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci Engn Comp, POB 2719, Beijing 100190, Peoples R China2.Univ Insubria, Dipartimento Sci & Alta Tecnol, I-22100 Como, Italy3.Grad Univ Adv Studies, SOKENDAI, Sch Multidisciplinary Sci, Natl Inst Informat,Chiyoda Ku, 2-1-2 Hitotsubashi, Tokyo 1018430, Japan4.Grad Univ Adv Studies, SOKENDAI, Sch Multidisciplinary Sci, Dept Informat,Chiyoda Ku, 2-1-2 Hitotsubashi, Tokyo 1018430, Japan5.Kent State Univ, Dept Math Sci, Kent, OH 44242 USA6.Tongji Univ, Dept Math, 1239 Siping Rd, Shanghai 200092, Peoples R China Recommended CitationGB/T 7714 Bai, Zhong-Zhi,Buccini, Alessandro,Hayami, Ken,et al. Modulus-based iterative methods for constrained Tikhonov regularization[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,2017,319:1-13. APA Bai, Zhong-Zhi,Buccini, Alessandro,Hayami, Ken,Reichel, Lothar,Yin, Jun-Feng,&Zheng, Ning.(2017).Modulus-based iterative methods for constrained Tikhonov regularization.JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,319,1-13. MLA Bai, Zhong-Zhi,et al."Modulus-based iterative methods for constrained Tikhonov regularization".JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 319(2017):1-13.
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