Official Course Description
This is an upgraded version of NUMA12 Numerical Approximation.
The fundamental problem of approximation theory is to represent a possibly complicated function by simpler, easier to compute functions.
In approximation theory it is usually assumed that the values of the function are available. This information is then used to construct an approximant.
In numerical computation, information usually comes in a less explicit form. For example, the function may be the solution to a differential equation. Nevertheless, the two subjects of approximation and computation are closely related, and it is impossible to fully understand the possibilities in numerical computations without a good understanding of the elements of constructive approximation. Furthermore, ap- proximation theory requires the acquisition of a basic understanding of operator theory and thus can serve as the first steps towards functional analysis.