Defines and investigates two families of dual polynomials for Gauss-Legendre polynomials to enable representations, dual bases for Lagrange interpolation, and approximation problem solutions in CAGD.
Evaluation of Gauss-Legendre curves
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abstract
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.
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2026 1verdicts
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Dual Gauss--Legendre polynomials
Defines and investigates two families of dual polynomials for Gauss-Legendre polynomials to enable representations, dual bases for Lagrange interpolation, and approximation problem solutions in CAGD.