Evaluation of Gauss-Legendre curves

Fuente: arXiv
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Main Authors: Chudy, Filip, Woźny, Paweł
Format: Preprint
Published: 2026
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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