HermiteInterpolation

fit(x, y, [y′, y″, ...])

Builds a polynomial fit to the sample points $x$ with labels $y$. The remaining, optional arguments may provide derivative data, $dⁿy/dxⁿ$ for $n = 1, … m-1$. The Hermite interpolation procedure returns a unique polynomial of degree less than $m n$. Absent derivative data ($m = 1$) the method reduces to Lagrange interpolation.

As an example, one can infer the function $y = x²$ from three labeled points:

f = HermiteInterpolation.fit([0, 1, 2], [0, 1, 4])
@assert f(3) ≈ 9

Or from a single point with derivative and curvature data:

f = HermiteInterpolation.fit([0], [0], [0], [2])
@assert f(3) ≈ 9

The fitting algorithm involves building a divided difference table, as described on Wikipedia.