Interpolation Error
When interpolating a given function f by a polynomial of degree n at the nodes x0,...,xn we get the error
where
is the notation for divided differences.
If f is n + 1 times continuously differentiable on a closed interval I and be a polynomial of degree at most n that interpolates f at n + 1 distinct points {xi} (i=0,1,...,n) in that interval. Then for each x in the interval there exists in that interval such that
Read more about this topic: Polynomial Interpolation
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