Remarks on numerical integration, discrepancy, and diaphony
arXiv:1711.070173 citationsh-index: 38
AI Analysis
Provides theoretical connections between two fields, but is purely theoretical with no empirical results.
The paper unifies formulations of numerical integration from approximation theory and discrepancy theory, and uses approximation theory techniques to prove lower bounds for smooth discrepancy.
The goal of this paper is twofold. First, we present a unified way of formulating numerical integration problems from both approximation theory and discrepancy theory. Second, we show how techniques, developed in approximation theory, work in proving lower bounds for recently developed new type of discrepancy -- the smooth discrepancy.