Geodesic
Sparse quadrature for high-dimensional integration with Gaussian measure
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 2, pp. 631-657

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In this work we analyze the dimension-independent convergence property of an abstract sparse quadrature scheme for numerical integration of functions of high-dimensional parameters with Gaussian measure. Under certain assumptions on the exactness and boundedness of univariate quadrature rules as well as on the regularity assumptions on the parametric functions with respect to the parameters, we prove that the convergence of the sparse quadrature error is independent of the number of the parameter dimensions. Moreover, we propose both an a priori and an a posteriori schemes for the construction of a practical sparse quadrature rule and perform numerical experiments to demonstrate their dimension-independent convergence rates.

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Accepté le :
DOI : 10.1051/m2an/2018012
Classification : 65C20, 65D30, 65D32, 65N12, 65N15, 65N21
Keywords: Uncertainty quantification, high-dimensional integration, curse of dimensionality, convergence analysis, Gaussian measure, sparse grids, a priori construction, a posteriori construction

Chen, Peng 1

1 
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     title = {Sparse quadrature for high-dimensional integration with {Gaussian} measure},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {631--657},
     publisher = {EDP-Sciences},
     volume = {52},
     number = {2},
     year = {2018},
     doi = {10.1051/m2an/2018012},
     mrnumber = {3834438},
     zbl = {06966736},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2018012/}
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Chen, Peng. Sparse quadrature for high-dimensional integration with Gaussian measure. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 2, pp. 631-657. doi: 10.1051/m2an/2018012

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