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Journal of Applied Mathematics
Volume 2015, Article ID 376362, 8 pages
http://dx.doi.org/10.1155/2015/376362
Research Article

A Smoothening Method for the Piecewise Linear Interpolation

Department of Statistics and Computer Science, Kunsan National University, Gunsan 573-701, Republic of Korea

Received 11 May 2015; Accepted 2 July 2015

Academic Editor: Xiao-wei Gao

Copyright © 2015 Beong In Yun. 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 propose a method to smoothen a piecewise linear interpolation at a small number of nodes on a bounded interval. The method employs a sigmoidal type weight function having a property that clusters most points on the left side of the interval toward 0 and those on the right side toward 1. The proposed method results in a noninterpolatory approximation which is smooth over the whole interval. We provide an algorithm for implementing the presented smoothening method. To demonstrate usefulness of the presented method we introduce some numerical examples and investigate the results.