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Let f ∈ C2 [a, b], and let the nodes a = x0 < x1 < · · · < xn = b be given. Derive an error estimate similar to that in Theorem 3.13 for the piecewise linear interpolating function F. Use this estimate to derive error bounds for Exercise 21.
In Exercise 21
Given the partition x0 = 0, x1 = 0.05, and x2 = 0.1 of [0, 0.1], find the piecewise linear interpolating function F for f (x) = e2x. Approximate
F(x) dx, and compare the results to the actual value. |
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