Table of Contents
Advances in Numerical Analysis
Volume 2014 (2014), Article ID 353194, 8 pages
http://dx.doi.org/10.1155/2014/353194
Research Article

Error Analysis for a Noisy Lacunary Cubic Spline Interpolation and a Simple Noisy Cubic Spline Quasi Interpolation

School of Mathematical Sciences, Ocean University of China, Qingdao, Shandong 266100, China

Received 18 May 2014; Revised 30 August 2014; Accepted 30 August 2014; Published 10 September 2014

Academic Editor: Weizhu Bao

Copyright © 2014 Feng-Gong Lang and Xiao-Ping Xu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We mainly present the error analysis for two new cubic spline based methods; one is a lacunary interpolation method and the other is a very simple quasi interpolation method. The new methods are able to reconstruct a function and its first two derivatives from noisy function data. The explicit error bounds for the methods are given and proved. Numerical tests and comparisons are performed. Numerical results verify the efficiency of our methods.