Adaptive points to estimate the Lebesgue constant on the simplex
Visualitza/Obre
Estadístiques de LA Referencia / Recolecta
Inclou dades d'ús des de 2022
Cita com:
hdl:2117/383623
Tipus de documentText en actes de congrés
Data publicació2022-05
EditorBarcelona Supercomputing Center
Condicions d'accésAccés obert
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continguts d'aquesta obra estan subjectes a la llicència de Creative Commons
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Reconeixement-NoComercial-SenseObraDerivada 4.0 Internacional
Abstract
We present a novel adaptive sampling method to estimate the Lebesgue constant of nodal sets in n-dimensional simplices. The main application of this estimation is to assess the interpolation capabilities of a nodal distribution. Given such distribution, the Lebesgue constant corresponds to the maximum of the Lebesgue function, which is non-differentiable. Thus, our method estimates the extremum by only evaluating the function values at a set of sample points that are successively adapted to seek the maximum. Remarkably, our adaptive search does not require storing a mesh to query neighbor points. Furthermore, the search automatically stops by considering specific spatial and Lipschitz-based criteria. The examples, up to four dimensions, show that the method is well-suited to estimate the Lebesgue constant of different nodal distributions.
CitacióJiménez Ramos, A.; Gargallo Peiró, A.; Roca, X. Adaptive points to estimate the Lebesgue constant on the simplex. A: . Barcelona Supercomputing Center, 2022, p. 53-54.
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9BSCDS_20_Adaptive points to.pdf | 1,293Mb | Visualitza/Obre |