1. Furthermore, the interpolant is a polynomial and thus infinitely differentiable. 2. This suffices to show that ? is a suitable interpolant in this case. 3. The nature of the interpolant circuit can be arbitrary. 4. Having S = 0 means the solution is the " natural " spline interpolant . 5. For example, the interpolant above has a local maximum at " x" 6. This clearly yields a bound on how well the interpolant can approximate the unknown function. 7. The interpolant is linear along lines quadratic. 8. In curve fitting problems, the constraint that the interpolant has to go exactly through the data points is relaxed. 9. The initial simplex must have at least one face which contains a zero of the unique linear interpolant on that face. 10. Another disadvantage is that the interpolant is not differentiable at the point " x " " k ".
