Open AccessComprehensive Interpretation of a Three-Point Gauss Quadrature with Variable Sampling Points and Its Application to Integration for Discrete Data
Author(s) -
Young-Doo Kwon,
Soon-Bum Kwon,
Bo-Kyung Shim,
Hyun-Wook Kwon
Publication year - 2013
Publication title -
journal of applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.307
H-Index - 43
eISSN - 1687-0042
pISSN - 1110-757X
DOI - 10.1155/2013/471731
Subject(s) - mathematics , gauss–kronrod quadrature formula , clenshaw–curtis quadrature , gaussian quadrature , numerical integration , quadrature (astronomy) , gauss–jacobi quadrature , weighting , tanh sinh quadrature , gauss , sampling (signal processing) , mathematical analysis , nyström method , computer science , integral equation , medicine , physics , engineering , filter (signal processing) , quantum mechanics , electrical engineering , computer vision , radiology
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
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