Function Interpolation
Overview
Function interpolation ake a set
of points, sampled from the functions domain with the corresponding function outputs, and tries to
create a function that fits the sample points. Interpolation is often justified by the
Weierstrass Approximation Theorem.
The Weierstrass Approximation Theorem states that for a function f that is continuous on an interval, there exists a
polynomial p such that
{% |f(x) - p(x)| < \epsilon %}
over that interval. (
komzsik pg.3)
Interpolation Methods
- Classical Interpolation : earliest methods developed by
luminaries such as Newton and Lagrange.
- Splines : are an effective way to interpolate a function.
Given a set of points for which the function value is known, a spline interpolates between those values, using an interpolating
function and a set of constraints.
