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.
![](https://test.transtutors.com/qimg/c03c7ccb-94c3-4671-aae7-d641cae42765.png)
![](https://test.transtutors.com/qimg/d5c7c8c1-8a87-4235-8c43-24b7e57269dd.png)