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


#1

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?


#2

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
manipulations.