High-order numerical integration on self-affine sets
Numerical Analysis
2025-12-16 v2 Numerical Analysis
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.
Cite
@article{arxiv.2410.00637,
title = {High-order numerical integration on self-affine sets},
author = {Patrick Joly and Maryna Kachanovska and Zoïs Moitier},
journal= {arXiv preprint arXiv:2410.00637},
year = {2025}
}