# Quadrature at fake nodes

@inproceedings{Marchi2021QuadratureAF, title={Quadrature at fake nodes}, author={Stefano De Marchi and Giacomo Elefante and Emma Perracchione and Davide Poggiali}, year={2021} }

We investigate the use of the so-called mapped bases or fake nodes approach in the framework of numerical integration. We show that such approach is able to mitigate the Gibbs phenomenon when integrating functions with steep gradients. Moreover, focusing on the optimal properties of the Chebyshev-Lobatto nodes, we are able to analytically compute the quadrature weights of the fake Chebyshev-Lobatto nodes. Such weights, quite surprisingly, coincide with the composite trapezoidal rule. Numerical…

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## 2 Citations

On Kosloff Tal-Ezer least-squares quadrature formulas

- Computer Science, MathematicsArXiv
- 2021

This work investigates the combination of the Kosloff Tal-Ezer map and Least-squares approximation for numerical quadrature and finds that some static choices of the map’s parameter improve the results of the composite trapezoidal rule, while a dynamic approach achieves larger stability and faster convergence, even when the sampling nodes are perturbed.

Stable discontinuous mapped bases: the Gibbs-Runge-Avoiding Stable Polynomial Approximation (GRASPA) method

- Mathematics, Computer ScienceComputational and Applied Mathematics
- 2021

This work proposes a novel approach, termed Gibbs-Runge-Avoiding Stable Polynomial Approximation (GRASPA), where both Runge’s and Gibbs phenomena are mitigated and a theoretical analysis of the Lebesgue constant associated to the mapped nodes is provided.

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