Question

For an nth-order Newton's divided difference interpolating polynomial fn(x), the error of interpolation can be estimated by Rn-| g(xmPX, , xm» ,&J . (x-x-Xx-x.) . . . (x-x.) | , where (xo, f(xo)), (xi, fx)).., (Xn-1, f(xn-1) are data points; g[x-,x,,x-.., x,] is the (n+1)-th finite divided difference. To minimize Rn, if there are more than n+1 data points available for calculating fn(x) using the nth-order Newton's interpolating polynomial, n+1 data points (Xo, f(xo)), (x1, f(x)), , (in, f(%)) should be chosen from the available data points such that l (x-x0)(x-%) . . . (x-x") | is the smallest. Given the data 3.2 2.4 5.6 7.8 6.2 12.5 7.3 16.6 8.0 12.5 8.5 6.5 Calculate f(7.0) using Newton's divided difference interpolating polynomials with n 3 Estimate the error R3 of f(7.0)

Answer 1

Solubie Griven that 323 808 Dividel difference table а. Ч 32 a.85 1 5.6 8 1.04 7.83 0-092 3.13 5-86 19 5.33 D452 7.3 6- 6 0.09 8.0

armula A 3+1 (sn) !

3 0- EXToY 0