Dimension-adaptive sparse grid quadrature for integrals with boundary singularities
Dimension-adaptive sparse grid quadrature for integrals with boundary singularities
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2013Verlag / herausgebende Einrichtung
Institut für Numerische Simulation (INS)Verlagsort
BonnMetadaten
Zur Langanzeige
Zitierbarer Link (Handle URI) 
https://hdl.handle.net/20.500.11811/11926
Inhalt
Classical Gaussian quadrature rules achieve exponential convergence for univariate functions that are infinitly smooth and where all derivatives are uniformly bounded. The aim of this paper is to construct generalized Gaussian quadrature rules based on non-polynomial basis functions, which yield exponential convergence even for integrands with (integrable) boundary singularities whose exact type is not a-priori known. Moreover, we use sparse tensor-products of these new formulae to compute d-dimensional integrands with boundary singularities by means of a dimension- adaptive approach. As application, we consider, besides standard model problems, the approximation of multivariate normal probabilities using the Genz-algorithm.
Klassifikation (DDC)
510 Mathematik 518 Numerische AnalysisErstpublikation
https://ins.uni-bonn.de/publication/preprintsZugehörige Publikation(en)
https://doi.org/10.1007/978-3-319-04537-5_5Reihe, Nummer
INS Preprints ; 1310Griebel, Michael; Oettershagen, Jens: Dimension-adaptive sparse grid quadrature for integrals with boundary singularities. In: INS Preprints, 1310.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11926
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11926
@unpublished{handle:20.500.11811/11926,
author = {{Michael Griebel} and {Jens Oettershagen}},
title = {Dimension-adaptive sparse grid quadrature for integrals with boundary singularities},
publisher = {Institut für Numerische Simulation (INS)},
year = 2013,
INS Preprints},
volume = 1310,
note = {Classical Gaussian quadrature rules achieve exponential convergence for univariate functions that are infinitly smooth and where all derivatives are uniformly bounded. The aim of this paper is to construct generalized Gaussian quadrature rules based on non-polynomial basis functions, which yield exponential convergence even for integrands with (integrable) boundary singularities whose exact type is not a-priori known. Moreover, we use sparse tensor-products of these new formulae to compute d-dimensional integrands with boundary singularities by means of a dimension- adaptive approach. As application, we consider, besides standard model problems, the approximation of multivariate normal probabilities using the Genz-algorithm.},
url = {https://hdl.handle.net/20.500.11811/11926}
}
author = {{Michael Griebel} and {Jens Oettershagen}},
title = {Dimension-adaptive sparse grid quadrature for integrals with boundary singularities},
publisher = {Institut für Numerische Simulation (INS)},
year = 2013,
INS Preprints},
volume = 1310,
note = {Classical Gaussian quadrature rules achieve exponential convergence for univariate functions that are infinitly smooth and where all derivatives are uniformly bounded. The aim of this paper is to construct generalized Gaussian quadrature rules based on non-polynomial basis functions, which yield exponential convergence even for integrands with (integrable) boundary singularities whose exact type is not a-priori known. Moreover, we use sparse tensor-products of these new formulae to compute d-dimensional integrands with boundary singularities by means of a dimension- adaptive approach. As application, we consider, besides standard model problems, the approximation of multivariate normal probabilities using the Genz-algorithm.},
url = {https://hdl.handle.net/20.500.11811/11926}
}
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