Use the hermite cubic basis functions 551 and 552 to

Question

Hermite Cubic Basis Function Expansion

Use the Hermite cubic basis functions (5.51) and (5.52) to approximate the function s² exp[s^-2 ] in the domain [-3, 3]. Begin with nodes at (-3,-2,-1,0, 1,2,3). Discretize the s -space with intervals of length 0.1, i.e. (-3.0,-2.9,-2.8,...), and approximate the function at these points. Choose more nodes at more discrete points and see how the fit improves. Provide graphs similar to those in Figures 5-6 and 5-7.