Abstract
There are many cases where one knows the value of a function at discrete points and wants to estimate the function's value between those points. That is, one wants to interpolate the function between the known values. In this chapter we review properties of polynomials and their properties of uniqueness and approximation. Then we show how a polynomial interpolating function can be constructed using the Lagrange polynomial formula. Polynomial interpolants are easy to construct but suffer from the Runge phenomenon where high-degree polynomials have unacceptable oscillations in the reconstruction. To deal with the Runge phenomenon, we present cubic splines as a way to get accurate interpolating functions in a straightforward way. We use SciPy's cubic spline functionality for this purpose.
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