Summary: BEST APPROXIMATION
Given a function f(x) that is continuous on a given
interval [a, b], consider approximating it by some poly-
nomial p(x). To measure the error in p(x) as an ap-
proximation, introduce
E(p) = max
axb
|f(x) - p(x)|
This is called the maximum error or uniform error of
approximation of f(x) by p(x) on [a, b].
With an eye towards efficiency, we want to find the
`best' possible approximation of a given degree n.
With this in mind, introduce the following:
n(f) = min
deg(p)n
E(p)
= min
deg(p)n
"
max

Source: Atkinson, Kendall - Departments of Computer Science & Mathematics, University of Iowa

Collections: Computer Technologies and Information Sciences