I was wondering how I could fit a polynomial surface through a set of points in two variables. When I look up this problem in the literature, I usually see two options:
- Use a tensor product, but this only seems to work in the case the points are evaluated in a grid
- Use some special point layouts, like Padua or Chebyshev points.
Neither options seems feasible for pseudo-random point sets. Does anyone have an idea? (I guess I could use the standard Lagrange formula in two variables, but that doesn't seem like a numerically stable solution.)