STOCHASTIC CONVERGENCE OF A NONCONFORMING FINITE ELEMENT METHOD FOR THE THIN PLATE SPLINE SMOOTHER FOR OBSERVATIONAL DATA

doi:10.1137/16M109630X

	STOCHASTIC CONVERGENCE OF A NONCONFORMING FINITE ELEMENT METHOD FOR THE THIN PLATE SPLINE SMOOTHER FOR OBSERVATIONAL DATA
	Chen, Zhiming1,2 ; Tuo, Rui3 ; Zhang, Wenlong 2
	2018
发表期刊	SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN	0036-1429
卷号	56 期号:2 页码:635-659
摘要	The 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.
关键词	thin plate spline Morley element stochastic convergence optimal parameter choice
DOI	10.1137/16M109630X
语种	英语
资助项目	China NSF[113211061]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000431189500001
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/30292
专题	计算数学与科学工程计算研究所系统科学研究所
通讯作者	Chen, Zhiming
作者单位	1.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
推荐引用方式 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.