Introduction
The Weierstrass approximation theorem states that every continuous function f(x) defined on an interval can be uniformly approximated as closely as desired by a polynomial function Pn(x) of degree ≤ n, i.e.,
Interpolation at equidistant points is a natural and well-known approach to construct approximating polynomials. Runge's phenomenon demonstrates, however, that interpolation can easily result in divergent approximations.
Read more about this topic: Runge's Phenomenon
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—Henry David Thoreau (1817–1862)
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