請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/30014完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳宜良(I-Liang Chern) | |
| dc.contributor.author | Yu-Chin Lin | en |
| dc.contributor.author | 林有慶 | zh_TW |
| dc.date.accessioned | 2021-06-13T01:30:40Z | - |
| dc.date.available | 2007-07-20 | |
| dc.date.copyright | 2007-07-20 | |
| dc.date.issued | 2007 | |
| dc.date.submitted | 2007-07-17 | |
| dc.identifier.citation | [1] Ming Jiang. Image Reconstruction, Processing and Analysis. Unpublished
[2] Richard L. Burden and J. Douglas Faires, Numerical Analysis,7th Edition, Brooks/Cole Publishing Company, 511 Forest Lodge Road, Pacific Grove, CA 93950, USA, 2001. [3] F. Natterer. The mathematics of computerized tomography. John Wiley & Sons, 2001. [4] C. Popa. Algebraic multigrid for general inconsistent linear systems: Preliminary results. Technical Report 06-2, Lehrstuhl fűr Informatik 10 (Systemsimulation), FAU Erlangen-Nűurnberg, 2006. [5] Popa C., On smoothing property of the SOR relaxation, Studii si Cercetari Matematice, 41(5)(1989), 399-406. [6] Popa C., Extensions of block-projections methods with relaxation parameters to inconsistent and rank-defficient least-squares problems; B I T, 38(1)(1998), 151-176. [7] Kőtler, Harald ; Popa, Constantin ; Prűmer, Marcus ; Rűde, Ulrich: Towards an Algebraic Multigrid Method for Tomographic Image Reconstruction - Improving Convergence of ART . In: Wesseling, P. ; Onate, E. ; Peiaux, J. (Hrsg.) : ECCOMAS CFD 06. [8]H. Kőstler, C. Popa, and U. Rűde. Algebraic multigrid for general inconsistent linear systems: The correction step. Technical Report 06-4, Lehrstuhl fűr Informatik 10 (Systemsimulation), FAU Erlangen-Nűrnberg, 2006. [9]William L. Briggs, A Multigrid Tutorial, SIAM, Philadelphia, Pennsylvania, 2000. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/30014 | - |
| dc.description.abstract | We are concerned with the algebraic multigrid (AMG) method for least square problem arisen from image restorations. We employ the Kaczmarz’s method as the smoothers for the AMG and prove the corresponding smoothing property. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-13T01:30:40Z (GMT). No. of bitstreams: 1 ntu-96-R94221031-1.pdf: 315120 bytes, checksum: f2e139bae16ac84558c767e6c3bc60f6 (MD5) Previous issue date: 2007 | en |
| dc.description.tableofcontents | Abstract vii
1 Introduction 1 2 CT and Radon transform 3 2.1 CT and Radon transform . . . . . . . . . . . . . . . . . . . . . 3 2.2 Discrete Radon transform . . . . . . . . . . . . . . . . . . . . 4 3 Kaczmarz’s Method and SOR method 7 3.1 Kaczmarz’s Method . . . . . . . . . . . . . . . . . . . . . . . . 7 3.2 SOR method . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.3 Kaczmarz method : a variant of SOR . . . . . . . . . . . . . . 10 3.4 Kaczmarz’s method for inverse Radon transform . . . . . . . . 12 4 Smoothing property of Kaczmarz’s method 15 4.1 Smoothing property of SOR method . . . . . . . . . . . . . . 16 4.2 Classical result . . . . . . . . . . . . . . . . . . . . . . . . . . 17 4.3 Consistent case . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.4 Inconsistent case . . . . . . . . . . . . . . . . . . . . . . . . . 22 5 Algebraic Multigrid for general inconsistnet linear system 29 | |
| dc.language.iso | en | |
| dc.subject | Kaczmarz法 | zh_TW |
| dc.subject | 代數多重網格法 | zh_TW |
| dc.subject | algebraic multigrid | en |
| dc.subject | smoothing property | en |
| dc.subject | Kaczmarz method | en |
| dc.subject | AMG | en |
| dc.title | 代數多重網格法與卡茨馬爾茲法 | zh_TW |
| dc.title | Algebraic Multigrid method of Kaczmarz method | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 95-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 薛克民(Keh-Ming Shyue),周謀鴻(Mo-Hong Chou) | |
| dc.subject.keyword | 代數多重網格法,Kaczmarz法, | zh_TW |
| dc.subject.keyword | algebraic multigrid,AMG,Kaczmarz method,smoothing property, | en |
| dc.relation.page | 36 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2007-07-17 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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