Lagrange Interpolation
The Lagrange interpolation formula is a way to find a polynomial which takes on certain values at arbitrary points. Specifically, it gives a constructive proof of the theorem below.
Suppose we have one point (1,3). How can we find a polynomial that could represent it?
Suppose we have sequence of points: (1,3), (2,4). How can we find a polynomial that could represent it?
Suppose we have sequence of points: (1,3), (2,4), (7,11). How can we find a polynomial that could represent it?In a general form it looks like this:
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