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Poly Interpolation: When would it be convenient to use Lagrange Basis?


Newton is preferred but for small n, we can use any of the three.

What’s an example of Lagrange bases being more convenient than monomials and Newton for small n?


When an explicit formula for polynomial interpolant is needed,
Lagrange is the choice.
Consider also the theorem about existence and uniqueness
of polynomial interpolant of deg <= n, for n+1 distinct points.
The existence is proved by the Lagrange form.
In general, Lagrange may be useful for certain mathematical