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A Numerical study of Newton interpolation with extremely high degrees

Michael Breuß, Friedemann Kemm, Oliver Vogel (2018)

Kybernetika

In current textbooks the use of Chebyshev nodes with Newton interpolation is advocated as the most efficient numerical interpolation method in terms of approximation accuracy and computational effort. However, we show numerically that the approximation quality obtained by Newton interpolation with Fast Leja (FL) points is competitive to the use of Chebyshev nodes, even for extremely high degree interpolation. This is an experimental account of the analytic result that the limit distribution of FL...

A weighted empirical interpolation method: a priori convergence analysis and applications

Peng Chen, Alfio Quarteroni, Gianluigi Rozza (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We extend the classical empirical interpolation method [M. Barrault, Y. Maday, N.C. Nguyen and A.T. Patera, An empirical interpolation method: application to efficient reduced-basis discretization of partial differential equations. Compt. Rend. Math. Anal. Num. 339 (2004) 667–672] to a weighted empirical interpolation method in order to approximate nonlinear parametric functions with weighted parameters, e.g. random variables obeying various probability distributions. A priori convergence analysis...

Is GPU the future of Scientific Computing ?

Georges-Henri Cottet, Jean-Matthieu Etancelin, Franck Perignon, Christophe Picard, Florian De Vuyst, Christophe Labourdette (2013)

Annales mathématiques Blaise Pascal

These past few years, new types of computational architectures based on graphics processors have emerged. These technologies provide important computational resources at low cost and low energy consumption. Lots of developments have been done around GPU and many tools and libraries are now available to implement efficiently softwares on those architectures.This article contains the two contributions of the mini-symposium about GPU organized by Loïc Gouarin (Laboratoire de Mathématiques d’Orsay),...

Kinetic BGK model for a crowd: Crowd characterized by a state of equilibrium

Abdelghani El Mousaoui, Pierre Argoul, Mohammed El Rhabi, Abdelilah Hakim (2021)

Applications of Mathematics

This article focuses on dynamic description of the collective pedestrian motion based on the kinetic model of Bhatnagar-Gross-Krook. The proposed mathematical model is based on a tendency of pedestrians to reach a state of equilibrium within a certain time of relaxation. An approximation of the Maxwellian function representing this equilibrium state is determined. A result of the existence and uniqueness of the discrete velocity model is demonstrated. Thus, the convergence of the solution to that...

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