For my numerical maths course I have to compare two types of interpolation:
Lagrange interpolation and piecewise (Lagrange) interpolation.
I've created codes in matlab for both and now I'm trying to explain what the advantages and disadvantages of both methods are...
I came to the conclusion that Lagrange interpolation (increasing the order of interpolation) needs less function calls than Piecewise interpolation (increasing the number of subintervals) for the same accuracy. I can't figure out what the (dis)advantages of both methods are, can someone help me with this question? This course sadly offers no book or other literature to look for possible answers.
Any help is appreciated!
Lagrange interpolation can easily introduce artificial oscillations. Consider for instance interpolating $f(x)=\frac{1}{1+25x^2}$ on equally spaced points on $[-1,1]$. You'll observe great oscillations as the number of points increases, which would not happen if you use lower order interpolation.