Improved approximations for the Rayleigh wave velocity in [-1, 0.5]
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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.
1992 ◽
Vol 108
(1)
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pp. 71-88
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2008 ◽
Vol 35
(3)
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pp. 201-205
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1996 ◽
Vol 100
(3)
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pp. 1542-1550
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1984 ◽
Vol 76
(5)
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pp. 1438-1444
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2007 ◽
Vol 18
(1)
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pp. 45-68
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2008 ◽
Vol 21
(4)
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pp. 337-352
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