MATLAB

Manually construct the divided-difference table for the interpolation problem in Example 10.7, which is shown below

2. 12 pts.] Manually construct the divided-difference table for the interpolation problem in Example 10.7, which is shown below Example 10.7: Manual Interpolation with Newton Polynomial Basis Use quadratic interpolation and the data presented in Example 10.2 on page 523 to estimate the viscosity of glycerin at 22 C. The interpolant is of the form Before any calculations are performed, one must decide which three support points will be used to define the interpolant. For T 22C, the "nearest" three points are at TI-10, T220, and T3 30. The relevant divided differences are fIT,- 1.492 -3.810 =-0.231 8 10 f[T;, = H3-142-0.629-1.492 -0.0863 10 f[T2, T3- f[Ti, T2] 0.0863+0.2318 = 7.2750 10 20 so that the interpolant formula becomes (T) 3.810 0.2318(T 10 7.2750 x 103(T - 10)(T - 20), Evaluating the interpolant at T = 22 gives a(22) 3.810-0.231 8(12) + 7.2750 x 10-3 ( 12) (2)-1 .2030 The result depends on the choice of the support points and the degree of the polynomial interpolant. (See Example 10.2 and Exercises 12 and 13)