Comparison of 2D Regular Lattices for the CPWL Approximation of Functions
Numerical Analysis
2025-02-06 v1 Numerical Analysis
Signal Processing
Abstract
We investigate the approximation error of functions with continuous and piecewise-linear (CPWL) representations. We focus on the CPWL search spaces generated by translates of box splines on two-dimensional regular lattices. We compute the approximation error in terms of the stepsize and angles that define the lattice. Our results show that hexagonal lattices are optimal, in the sense that they minimize the asymptotic approximation error.
Cite
@article{arxiv.2502.03115,
title = {Comparison of 2D Regular Lattices for the CPWL Approximation of Functions},
author = {Mehrsa Pourya and Maïka Nogarotto and Michael Unser},
journal= {arXiv preprint arXiv:2502.03115},
year = {2025}
}