Paper
High-order numerical integration on self-affine sets
Authors
Patrick Joly, Maryna Kachanovska, Zoïs Moitier
Abstract
We construct an interpolatory high-order cubature rule to compute integrals of smooth functions over self-affine sets with respect to an invariant measure. The main difficulty is the computation of the cubature weights, which we characterize algebraically, by exploiting a self-similarity property of the integral. We propose an -version and a -version of the cubature, present an error analysis and conduct numerical experiments.