Numerical Method20815 marksNumerical: Newton's interpolation formulaNewton's Interpolation using divided differences, forward di
Consider the following data points. Estimate f(0.6) using Newton's interpolation formula.
Consider the following data points. Estimate $f(0.6)$ using Newton's interpolation formula.
$$\begin{array}{c|ccccc} x & 0.1 & 0.2 & 0.3 & 0.4 & 0.5 \ \hline f(x) & 2.68 & 3.04 & 3.38 & 3.69 & 3.97 \end{array}$$
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x 0.1 0.2 0.3 0.4 0.5 ---------------------------- f(x) 2.68 3.04 3.38 3.69 3.97 - Step size $h = 0.1$ (equally spaced) - Target: $f(0.6)$ Since $x = 0.6$ lies beyond the last point $x = 0.5$, use Newton's Backward Difference Formula with base $xn = 0.5$. --- x f(x) ∇f ∇²f ∇³f ∇⁴f ---------------...