Improved approximations for the Rayleigh wave velocity in [-1, 0.5]
In the present paper we derive improved approximations for the Rayleigh wave velocity in the interval \(\nu \in \) [−1, 0.5] using the method of least squares. In particular: (i) We create approximate polynomials of order 4, 5, 6 whose maximum percentage errors are 0.035 %, 0.015 %, 0.0083 %, respe...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Publishing House for Science and Technology
2008-12-01
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| Series: | Vietnam Journal of Mechanics |
| Online Access: | https://vjs.ac.vn/index.php/vjmech/article/view/5640 |
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| Summary: | In the present paper we derive improved approximations for the Rayleigh wave velocity in the interval \(\nu \in \) [−1, 0.5] using the method of least squares. In particular: (i) We create approximate polynomials of order 4, 5, 6 whose maximum percentage errors are 0.035 %, 0.015 %, 0.0083 %, respectively. (2i) Improved approximations in the form of the inverse of polynomials of order 3, 5 are also established. They are approximations with very high accuracy. (3i) By using the best approximate second-order polynomial of the cubic power in the space \(C\)[0.474572, 0.912622], we derive an approximation that is the best, so far, of the approximations obtained by approximating the secular equation. |
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| ISSN: | 0866-7136 2815-5882 |