“Range Functions with High Approximation Orders”
Mercoledì 25 Febbraio 2026, 0re 14:30 - Aula 1BC45 - Kai Hormann (Università della Svizzera Italiana)
Abstract
Let $f : \mathbb{R}^n \to \mathbb{R}$ be a continuous multivariate real function. Determining the exact range $f(X) = \{ f(x) : x \in X \} = [a,b]$ of a compact, connected set $X \subset \mathbb{R}^n$ is impossible in general and requires using numerical approximation methods. If $X$ is a box, that is, $X = [a_1,b_1] \times \cdots \times [a_n,b_n]$, then it is possible to define so-called range functions $▯f$, which are based on interval arithmetic and guaranteed to approximate the range conservatively, $▯f(X) \supseteq f(X)$. The quality of this approximation is characterized by the approximation order of $▯f$, and classical constructions are limited to quadratic approximation orders.
In this talk, I will present several approaches to define range functions with higher approximation orders, discuss some implementation issues, and highlight potential applications.
