# Interpolation

Given a function $$f$$ and a set of values $$x_i$$, interpolation is the creation of a curve that passes through the points $$\left(x_i, f\left(x_i\right)\right)$$ which is used to approximate the function within the intervals defined by adjacent pairs of the values, typically because only a sample of the function is known.

One of the simplest approaches is linear interpolation in which the adjacent points are connected by straight lines
$f(x) \approx f(x_i) + \frac{x-x_i}{x_{i+1}-x_i}\left(f\left(x_{i+1}\right)-f\left(x_i\right)\right)$
for $$x$$ in $$\left[x_i, x_{i+1}\right]$$.

### Gallimaufry

 AKCalc ECMA Endarkenment Turning Sixteen

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