a.k. from thus spake a.k.
A few years ago we saw how we could approximate a function f between pairs of points (xi, f(xi)) and (xi+1, f(xi+1)) by linear and cubic spline interpolation which connect them with straight lines and cubic polynomials respectively, the latter of which yield smooth curves at the cost of somewhat arbitrary choices about their exact shapes.
An alternative approach is to construct a single function that passes through all of the points and, given that nth order polynomials are uniquely defined byn+1 values at distinct xi , it's tempting to use them.
An alternative approach is to construct a single function that passes through all of the points and, given that nth order polynomials are uniquely defined by