[20 points] Compute the divided-difference table for the tabulated function. Write down the Newton polynomial Pa(x) Evaluate Pa(x) at X-2.5 and X=3.5. The underlying function for the data is f(x)-3.6/x. Compare the function values x-2.5 and X=3.5 with the actual function values (calculate the percent true error). Xk 3.6 1.8 1.2 0.9 0.72 2 3 4 5 3 f(Xu)
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Step 1
First, we need to compute the divided-difference table for the given data. The given data is: | Xk | f(Xk) | |-----|-------| | 2 | 3.6 | | 3 | 1.8 | | 4 | 1.2 | | 5 | 0.9 | Now, we compute the divided differences: | Xk | f(Xk) | f[x1, x0] | Show moreā¦
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Let us given f(x) = e^-x and the table k xk f(xk) 0 1.0 1.00000 1 2.0 0.36788 2 3.0 0.13534 3 4.0 0.04979 4 5.0 0.01832 a) Compute the divided-difference table for the tabulated function. b) Write down the Newton polynomials P1(x), P2(x), P3(x), and P4(x). c) Evaluate the Newton polynomials in part (b) at x = 0.5. d) Compare the values in part (c) with the actual function value f(x).
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