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Bibliographic Details
Main Authors: Pourya, Mehrsa, Nogarotto, Maïka, Unser, Michael
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2502.03115
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author Pourya, Mehrsa
Nogarotto, Maïka
Unser, Michael
author_facet Pourya, Mehrsa
Nogarotto, Maïka
Unser, Michael
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2502_03115
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Comparison of 2D Regular Lattices for the CPWL Approximation of Functions
Pourya, Mehrsa
Nogarotto, Maïka
Unser, Michael
Numerical Analysis
Signal Processing
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.
title Comparison of 2D Regular Lattices for the CPWL Approximation of Functions
topic Numerical Analysis
Signal Processing
url https://arxiv.org/abs/2502.03115