> There are many techniques to interpolate between a given set of points. Polynomial interpolation can perfectly fit N points with an N-1 degree polynomial, but this approach can be problematic for large a N; high-degree polynomials tend to overfit their data, and suffer from other numerical issues like Runge's phenomenon.
This is a misconception that's often repeated. High degree polynomial interpolations are problematic if you use equispaced points. If you use Chebyshev points, they are highly accurate and in general perform much better than cubic splines. See myth 1 from Lloyd Trefethen's paper: https://people.maths.ox.ac.uk/trefethen/mythspaper.pdf
This is a misconception that's often repeated. High degree polynomial interpolations are problematic if you use equispaced points. If you use Chebyshev points, they are highly accurate and in general perform much better than cubic splines. See myth 1 from Lloyd Trefethen's paper: https://people.maths.ox.ac.uk/trefethen/mythspaper.pdf