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Journal of Applied Mathematics
Volume 2013, Article ID 471731, 8 pages
http://dx.doi.org/10.1155/2013/471731
Research Article

Comprehensive Interpretation of a Three-Point Gauss Quadrature with Variable Sampling Points and Its Application to Integration for Discrete Data

1School of Mechanical Engineering & IEDT, Kyungpook National University, Daegu 702-701, Republic of Korea
2Department of Mechanical Engineering, Pohang College, Pohang 791-711, Republic of Korea
3System Solution Research Department, Research Institute of Industrial Science & Technology, Pohang 790-600, Republic of Korea

Received 2 September 2013; Revised 27 November 2013; Accepted 28 November 2013

Academic Editor: Vit Dolejsi

Copyright © 2013 Young-Doo Kwon et al. 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

This study examined the characteristics of a variable three-point Gauss quadrature using a variable set of weighting factors and corresponding optimal sampling points. The major findings were as follows. The one-point, two-point, and three-point Gauss quadratures that adopt the Legendre sampling points and the well-known Simpson’s 1/3 rule were found to be special cases of the variable three-point Gauss quadrature. In addition, the three-point Gauss quadrature may have out-of-domain sampling points beyond the domain end points. By applying the quadratically extrapolated integrals and nonlinearity index, the accuracy of the integration could be increased significantly for evenly acquired data, which is popular with modern sophisticated digital data acquisition systems, without using higher-order extrapolation polynomials.