# Gaussian quadrature rules for $C^1$ quintic splines

@article{Bartovn2015GaussianQR, title={Gaussian quadrature rules for \$C^1\$ quintic splines}, author={Michael Bartovn and Rachid Ait-Haddou and Victor M. Calo}, journal={arXiv: Numerical Analysis}, year={2015} }

We provide explicit expressions for quadrature rules on the space of $C^1$ quintic splines with uniform knot sequences over finite domains. The quadrature nodes and weights are derived via an explicit recursion that avoids an intervention of any numerical solver and the rule is optimal, that is, it requires the minimal number of nodes. For each of $n$ subintervals, generically, only two nodes are required which reduces the evaluation cost by $2/3$ when compared to the classical Gaussian…

## 8 Citations

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These closed formulae are based on the semi-classical Jacobi type orthogonal polynomials and are explicit in the sense, that they compute the nodes and their weights in the first/last boundary subinterval and, via a recursion the other nodes/weights, parsing from the first-last subintervals to the “middle” of the interval.

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