I'm studying interpolation and I see that if you have 2 points you use a 3rd-degree polynomial and likewise a 6th degree polynomial for five points. Is this a general formula, and if so, what is it called( and how to prove it)?
These are the interpolation techniques I'm looking to learn:
- Naive interpolation
- Newtonian interpolation
- Lagrange interpolation
- Hermite interpolation Horner's algorithm
Please help me develop my understanding of these methods more than just memorizing a formula.