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 …

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.

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 answer is all …

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 functions.

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.

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 as good as …

Jan 4, 2022 · In this course, most of the effort will be spent on designing approximation algorithms for NP-hard problems. A formal definition follows in the next bullet point.