Repository: Freie Universit├Ąt Berlin, Math Department

Application of dimension truncation error analysis to high-dimensional function approximation To appear in: 2022. Springer Verlag, 2024.

Guth, Philipp A. and Kaarnioja, Vesa (2024) Application of dimension truncation error analysis to high-dimensional function approximation To appear in: 2022. Springer Verlag, 2024. In: Monte Carlo and Quasi-Monte Carlo Methods. Springer Verlag. (Submitted)

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Abstract

Parametric mathematical models such as parameterizations of partial differential equations with random coefficients have received a lot of attention within the field of uncertainty quantification. The model uncertainties are often represented via a series expansion in terms of the parametric variables. In practice, this series expansion needs to be truncated to a finite number of terms, introducing a dimension truncation error to the numerical simulation of a parametric mathematical model. There have been several studies of the dimension truncation error corresponding to different models of the input random field in recent years, but many of these analyses have been carried out within the context of numerical integration. In this paper, we study the L2 dimension truncation error of the parametric model problem. Estimates of this kind arise in the assessment of the dimension truncation error for function approximation in high dimensions. In addition, we show that the dimension truncation error rate is invariant with respect to certain transformations of the parametric variables. Numerical results are presented which showcase the sharpness of the theoretical results.

Item Type:Book Section
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > Deterministic and Stochastic PDEs Group
ID Code:3103
Deposited By: Ulrike Eickers
Deposited On:19 Feb 2024 15:28
Last Modified:19 Feb 2024 15:28

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