Numerical Method20815 marksNumerical: Cubic spline interpolationCubic spline interpolation
Given the data points below, find cubic spline which belongs to 1 leq x leq 3 and estimate f(2) using cubic splines.
Given the data points below, find cubic spline which belongs to $1 \leq x \leq 3$ and estimate $f(2)$ using cubic splines.
$$\begin{array}{c|ccc} x & 1.0 & 3.0 & 4.0 \ \hline f(x) & 1.5 & 4.5 & 9.0 \end{array}$$
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i $xi$ $fi$ ----------------- 0 1.0 1.5 1 3.0 4.5 2 4.0 9.0 Number of intervals $n = 2$. We use natural cubic spline (standard assumption when no end conditions given). --- $$h0 = x1 - x0 = 2, \qquad h1 = x2 - x1 = 1$$ Natural boundary conditions: $M0 = 0,\ M2 = 0$. Interior equation at $i=1$: $$...