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STOCHASTIC CONVERGENCE OF A NONCONFORMING FINITE ELEMENT METHOD FOR THE THIN PLATE SPLINE SMOOTHER FOR OBSERVATIONAL DATA
Chen, Zhiming1,2; Tuo, Rui3; Zhang, Wenlong2
2018
Source PublicationSIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN0036-1429
Volume56Issue:2Pages:635-659
AbstractThe thin plate spline smoother is a classical model for finding a smooth function from the knowledge of its observation at scattered locations which may have random noises. We consider a nonconforming Morley finite element method to approximate the model. We prove the stochastic convergence of the finite element method which characterizes the tail property of the probability distribution function of the finite element error. We also propose a self-consistent iterative algorithm to determine the smoothing parameter based on our theoretical analysis. Numerical examples are included to confirm the theoretical analysis and to show the competitive performance of the self consistent algorithm for finding the smoothing parameter.
Keywordthin plate spline Morley element stochastic convergence optimal parameter choice
DOI10.1137/16M109630X
Language英语
Funding ProjectChina NSF[113211061]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000431189500001
PublisherSIAM PUBLICATIONS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/30292
Collection计算数学与科学工程计算研究所
系统科学研究所
Affiliation1.Univ Chinese Acad Sci, Chinese Acad Sci, Acad Math & Syst Sci, LSEC,Inst Computat Math, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Chinese Acad Sci, Sch Math Sci, Beijing 100190, Peoples R China
3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Chen, Zhiming,Tuo, Rui,Zhang, Wenlong. STOCHASTIC CONVERGENCE OF A NONCONFORMING FINITE ELEMENT METHOD FOR THE THIN PLATE SPLINE SMOOTHER FOR OBSERVATIONAL DATA[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2018,56(2):635-659.
APA Chen, Zhiming,Tuo, Rui,&Zhang, Wenlong.(2018).STOCHASTIC CONVERGENCE OF A NONCONFORMING FINITE ELEMENT METHOD FOR THE THIN PLATE SPLINE SMOOTHER FOR OBSERVATIONAL DATA.SIAM JOURNAL ON NUMERICAL ANALYSIS,56(2),635-659.
MLA Chen, Zhiming,et al."STOCHASTIC CONVERGENCE OF A NONCONFORMING FINITE ELEMENT METHOD FOR THE THIN PLATE SPLINE SMOOTHER FOR OBSERVATIONAL DATA".SIAM JOURNAL ON NUMERICAL ANALYSIS 56.2(2018):635-659.
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