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Stochastic Convergence of a Nonconforming Finite Element Method for the Thin Plate Spline Smoother for Observational Data

Research paper by Zhiming Chen, Rui Tuo, Wenlong Zhang

Indexed on: 01 Jun '18Published on: 08 Mar '18Published in: SIAM journal on numerical analysis



Abstract

SIAM Journal on Numerical Analysis, Volume 56, Issue 2, Page 635-659, January 2018. 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.