(a) For the given data construct divided difference table and corresponding divided difference polynomial. Interpolate at x = 3.44. (b) For the given data construct Lagrange's interpolation polynomial. Interpolate at x = 3.44. (c) Compare the results obtained in part (a) and part (b). x 3.20 3.30 3.35 3.40 3.50 3.60 3.65 3.70 F(x 0.3125 0.303030 0.298507 0.294118 0.285714 0.277778 0.273 0.27 ) 973 0270
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To construct the divided difference table, we use the given data points: x | f(x) -------------- 3.20 | 0.312 3.30 | 0.303030 3.35 | 0.298507 3.40 | 0.294118 3.50 | 0.285714 3.60 | 0.277778 3.65 | 0.273 3.70 | 0.270973 The divided difference table 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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