Evaluation of Gauss-Legendre curves
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914488672845824 |
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| author | Chudy, Filip Woźny, Paweł |
| author_facet | Chudy, Filip Woźny, Paweł |
| contents | We present new representations of Gauss--Legendre polynomials and their derivatives in the shifted power basis and in bases related to symmetric orthogonal Jacobi polynomials. Using these representations and certain recurrence relations, we propose efficient $O(n^2+dn)$ methods for evaluating a Gauss--Legendre curve of degree $n$ in $\mathbb E^d$. We also propose algorithms for multipoint evaluation with computational complexity $O(Mdn+dn^2)$, where $M$ is the number of evaluation points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_17331 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Evaluation of Gauss-Legendre curves Chudy, Filip Woźny, Paweł Numerical Analysis Graphics We present new representations of Gauss--Legendre polynomials and their derivatives in the shifted power basis and in bases related to symmetric orthogonal Jacobi polynomials. Using these representations and certain recurrence relations, we propose efficient $O(n^2+dn)$ methods for evaluating a Gauss--Legendre curve of degree $n$ in $\mathbb E^d$. We also propose algorithms for multipoint evaluation with computational complexity $O(Mdn+dn^2)$, where $M$ is the number of evaluation points. |
| title | Evaluation of Gauss-Legendre curves |
| topic | Numerical Analysis Graphics |
| url | https://arxiv.org/abs/2604.17331 |