However, in many circumstances, you have equispaced nodes (not Chebyshev nodes), for which global polynomial interpolation is terrible and it is literally impos

However, in many circumstances, you have equispaced nodes (not Chebyshev nodes), for which global polynomial interpolation is terrible and it is literally impossible to make a global method which is without pitfalls. Trefethen has some other papers about this, esp. http://people.maths.ox.ac.uk/~trefethen/impossibility.pdf http://people.maths.ox.ac.uk/~trefethen/impossibility.pdf, but also a new paper in 2023 with a different recommended method ("AAA") https://link.springer.com/article/10.1007/s10543-023-00959-x https://link.springer.com/article/10.1007/s10543-023-00959-x In some cases cubic splines are a convenient and good enough tool, computationally cheap because the tridiagonal system involved can be solved in linear time.