Comprehensive Interpretation of a Three-Point Gauss Quadrature with Variable Sampling Points and Its Application to Integration for Discrete Data
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 poi...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/471731 |
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| author | Young-Doo Kwon Soon-Bum Kwon Bo-Kyung Shim Hyun-Wook Kwon |
| author_facet | Young-Doo Kwon Soon-Bum Kwon Bo-Kyung Shim Hyun-Wook Kwon |
| author_sort | Young-Doo Kwon |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-38025232db8146f9bf34cd240da5e311 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-38025232db8146f9bf34cd240da5e3112025-02-03T06:07:23ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/471731471731Comprehensive Interpretation of a Three-Point Gauss Quadrature with Variable Sampling Points and Its Application to Integration for Discrete DataYoung-Doo Kwon0Soon-Bum Kwon1Bo-Kyung Shim2Hyun-Wook Kwon3School of Mechanical Engineering & IEDT, Kyungpook National University, Daegu 702-701, Republic of KoreaSchool of Mechanical Engineering & IEDT, Kyungpook National University, Daegu 702-701, Republic of KoreaDepartment of Mechanical Engineering, Pohang College, Pohang 791-711, Republic of KoreaSystem Solution Research Department, Research Institute of Industrial Science & Technology, Pohang 790-600, Republic of KoreaThis 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.http://dx.doi.org/10.1155/2013/471731 |
| spellingShingle | Young-Doo Kwon Soon-Bum Kwon Bo-Kyung Shim Hyun-Wook Kwon Comprehensive Interpretation of a Three-Point Gauss Quadrature with Variable Sampling Points and Its Application to Integration for Discrete Data Journal of Applied Mathematics |
| title | Comprehensive Interpretation of a Three-Point Gauss Quadrature with Variable Sampling Points and Its Application to Integration for Discrete Data |
| title_full | Comprehensive Interpretation of a Three-Point Gauss Quadrature with Variable Sampling Points and Its Application to Integration for Discrete Data |
| title_fullStr | Comprehensive Interpretation of a Three-Point Gauss Quadrature with Variable Sampling Points and Its Application to Integration for Discrete Data |
| title_full_unstemmed | Comprehensive Interpretation of a Three-Point Gauss Quadrature with Variable Sampling Points and Its Application to Integration for Discrete Data |
| title_short | Comprehensive Interpretation of a Three-Point Gauss Quadrature with Variable Sampling Points and Its Application to Integration for Discrete Data |
| title_sort | comprehensive interpretation of a three point gauss quadrature with variable sampling points and its application to integration for discrete data |
| url | http://dx.doi.org/10.1155/2013/471731 |
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