.png){kind=icon}
.png){kind=icon}
Return
EFFICIENT IMPLEMENTATIONS OF THE MULTIVARIATE DECOMPOSITION METHOD FOR APPROXIMATING INFINITE-VARIATE INTEGRALS
.png){kind=icon}
OA
AI
DOI：10.1137/17M1161890.png)
.png){kind=icon}
.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
In this paper we focus on efficient implementations of the multivariate decomposition method (MDM) for approximating integrals of infinity-variate functions. Such infinity-variate integrals occur, for example, as expectations in uncertainty quantification. Starting with the anchored decomposition f = Sigma(u subset of N) f(u), where the sum is over all finite subsets of N and each f(u) depends only on the variables x(j) with j is an element of u, our MDM algorithm approximates the integral of f by first truncating the sum to some active set and then approximating the integral of the remaining functions f(u) term-byterm using Smolyak or (randomized) quasi-Monte Carlo quadratures. The anchored decomposition allows us to compute f(u) explicitly by function evaluations of f. Given the specification of the active set and theoretically derived parameters of the quadrature rules, we exploit structures in both the formula for computing f(u) and the quadrature rules to develop computationally efficient strategies to implement the MDM in various scenarios. In particular, we avoid repeated function evaluations at the same point. We provide numerical results for a test function to demonstrate the effectiveness of the algorithm.
Keywords:
quadrature
infinite-variate integral
multivariate decomposition method
quasi-Monte Carlo
Smolyak's method
sparse grids
AI Summary
Key information extracted from the uploaded paper, including a brief overview, abstract, background, key highlights, visual analysis, and future outlook.
Journal
IF:
2.6
Papers:
5.1K
Citations:
1.8W