Linear programming is an extremely versatile technique for designing approximation algorithms, because it is one of the most general and expressive problems that we know how to solve in …

Since this is a richer class of functions than polynomials — rational functions with q(x) 1 are polynomials, we expect that rational approximation of degree N gives results that are at least …

If approximation is our goal, interpolation is only one means to that end. In this chapter we investigate alternative approaches that directly optimize the quality of the approximation.

Approximation theory is an established field, and my aim is to teach you some of its most important ideas and results, centered on classical topics re-lated to polynomials and rational …

First, how can approximate mod els be at all useful? Should we not strive for exactness? Second, what makes some models more useful than others? On the first question: An approximate …

The idea behind approximation is to simplify complicated mathematical expressions. So, approximation is often used as a tool in estimation, but also in full-blown calculations.

In order to use an approximation intelligently, we need to be able to estimate the size of the error, which is the difference between the exact answer (which we do not know) and the …