1. Fit the following data below using Cubic Regression, Newton's Interpolating Polynomial and Lagrange Interpolating polynomial respectively. Terminate if Ea ? 0.0001 \begin{tabular}{|c|c|c|c|c|} \hline x & 1.6 & 2 & 2.5 & 3.2 \\ \hline f(x) & 2 & 8 & 14 & 15 \\ \hline \end{tabular}
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6 2 2 8 6 2.5 14 6 0 3.2 15 1 -5 -5 Now, let's calculate the coefficients for the Newton's Interpolating Polynomial: f[x0] = f(1.6) = 2 f[x0,x1] = Δf(x0) / Δx = 6 / (2 - 1.6) = 30 f[x0,x1,x2] = Δ^2f(x0) / (Δx * Δx) = 0 Show more…
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