Lower bounds in numerical mathematics

Abstract: In the analysis of algorithms, there is usually a big difference between upper and lower bounds. Upper bounds (on the running time, memory used or necessary input information) is usually achieved by a construction of an efficient algorithm. On the other hand, lower bounds show that the construction of better and better algorithms has some natural limits. We study lower bounds on the amount of input information needed for algorithms in numerical analysis. The problems discussed include numerical integration, signal processing, and discrete geometry. Naturally, we encounter connections to functional analysis, probability, and combinatorics.

Computer scienceMathematics

Audience: researchers in the topic

Modelling of materials - theory, model reduction and efficient numerical methods (UNCE MathMAC)