Use Newton’s interpolating polynomial to determine y at x = 3.5 to the best possible accuracy. Compute the finite divided differences as in Fig. 17.5, and order your points to attain optimal accuracy and convergence.

17.2 Use Newton’s interpolating polynomial to determine y at x = 3.5 to the best possible accuracy. Compute the finite divided differences as in Fig. 17.5, and order your points to attain optimal accuracy and convergence. That is, the points should be centered around and as close as possible to the unknown.
x 0 1 2.5 3 4.5 5 6
y 2 5.4375 7.3516 7.5625 8.4453 9.1875 12

 

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