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The continuous and differentiable PMID is constructed with discretely defined sampling points of the PMID using the cubic spline interpolation.
This is achieved by using the cubic spline shape functions and by introducing two new Lagrange terms in the variational principle.
Fengler [5] proposed a procedure based on quadratic programming using the cubic spline smoothing on the call price data to get an arbitrage-free implied volatility.
The main reason is that EMD extracts IAs using the cubic spline approach, rather than using more smooth local means and local magnitudes in LMD.
Fyfe [3], Jain et al. [4, 5], Al-Said [6, 7], Khan et al. [8] and Kadalbajoo et al. [9] have studied the solution of two point boundary value problems by using the cubic spline method.
By using the estimated (hat {h}_{l}(m)) at every symbol, the CIR at every sampling time (hat {h}_{l}(m,n_{2})) can be estimated by using the cubic spline interpolation method over one frame.
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In addition to this, in Table 4, the solutions are compared with the numerical solutions computed by using the Cubic splines (CS) in [21].
Step 2. Compute the upper and lower envelopes u i, j)(t) and 1 i, j)(t) by interpolating the local minimum and maximum using the cubic splines interpolation.
The plots were generated with the graphical interface MareyMapGUI and the slope of the curve was obtained using the "cubic splines" interpolation method.
To approximate the irregular geometries of limb buds, we used the cubic spline interpolation technique of de Boor [83].
We also used the cubic spline method to interpolate additional time points within the microarray data to avoid over-fitting.
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