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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.03115 |
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| _version_ | 1866913679334703104 |
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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 |