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

abstract

• 2018 Society for Industrial and Applied Mathematics. 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.

authors

• Tuo, Rui

published proceedings

• SIAM JOURNAL ON NUMERICAL ANALYSIS

author list (cited authors)

• Chen, Z., Tuo, R., & Zhang, W.

citation count

• 6

complete list of authors

• Chen, Zhiming||Tuo, Rui||Zhang, Wenlong

publication date

• January 2018

publisher

• Society for Industrial & Applied Mathematics (SIAM)  Publisher

published in

• SIAM Journal on Numerical Analysis  Journal

keywords

• Morley Element
• Optimal Parameter Choice
• Stochastic Convergence
• Thin Plate Spline

Digital Object Identifier (DOI)

• 10.1137/16M109630X

start page

• 635

end page

• 659

volume

• 56

issue

• 2

URL

• http://dx.doi.org/10.1137/16m109630x