Question: Use n + 1 equally spaced data points to interpolate f(t) = 1/(1 + t2) on an interval -a t a for a

Use n + 1 equally spaced data points to interpolate f(t) = 1/(1 + t2) on an interval -a ≤ t ≤ a for a = 1, 1.5, 2. 2.5, 3, and n = 2, 4. 10. 20. Do all intervals exhibit the pathology illustrated in Figure 4.10? If not. how large can a be before the inter-polants have poor approximation properties? What happens when the number of interpolation points is taken to be n = 50?

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