In numerical analysis, the Lagrange Polynomials are used for polynomial
interpolation.
"Given a set of distinct points {xⱼ,yⱼ}, the Lagrange Polynomial is the
[unique] polynomial of least degree such that at each point xⱼ assumes the
corresponding value yⱼ (i.e. the functions coincide at each point)."
The lagrange polynomials belong to a collection of techniques that
interpolate a function or a set of values, producing a continuous polynomial.
We can either directly supply a set of inputs and their corresponding outputs
for said function, or if we explicitly know the function, we can define it as
a callback function and then generate a set of points by evaluating that
function at n points between a start and end point. We then use these values
to interpolate a Lagrange polynomial.
https://en.wikipedia.org/wiki/Lagrange_polynomial
http://mathworld.wolfram.com/LagrangeInterpolatingPolynomial.html