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Polynomial Interpolation Question

16. Let P_2(x) be the quadratic polynomial interpolating f(x) at the evenly space point x_0, x_1 = x_0 + h, x_2 = x_0 + 2h. Derive formulas for the error:

f'(x_i) - P'_2(x_i), i = not zero, 1, 2

Assume f(x) is three times continuously differentiable, give commutable bounds for these errors.

Hint: use the error formula

f(t) - P_n(t) = (t - x_0) ... (t - x_n)f[x_0, ..., X_n, t]


Solution Summary

In a written JPG file, this solution goes step by step through finding the formulas for the error.