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
Famous quotes containing the word error:
“It is an error to believe that the Roman Pontiff can and ought to reconcile himself to, and agree with, progress, liberalism, and contemporary civilization.”
—Pope Pius IX (17921878)