What are the advantages and disadvantages of piecewise linear interpolation, cubic interpolation, and cubic spline interpolation?
I know that piecewise linear interpolation is not smooth and may not be accurate for nonlinear functions. The other two are smooth.
But I think my understanding is a little superficial. Especially the difference between the cubic interpolation and cubic spline though I know how to compute them. Could someone help me understanding the advantages and disadvantages of these three? Thanks so much!