Matches in SemOpenAlex for { <https://semopenalex.org/work/W4298380587> ?p ?o ?g. }
Showing items 1 to 83 of
83
with 100 items per page.
- W4298380587 abstract "In this paper we focus on efficient implementations of the Multivariate Decomposition Method (MDM) for approximating integrals of $infty$-variate functions. Such $infty$-variate integrals occur for example as expectations in uncertainty quantification. Starting with the anchored decomposition $f = sum_{mathfrak{u}subsetmathbb{N}} f_mathfrak{u}$, where the sum is over all finite subsets of $mathbb{N}$ and each $f_mathfrak{u}$ depends only on the variables $x_j$ with $jinmathfrak{u}$, 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 $f_mathfrak{u}$ term-by-term using Smolyak or (randomized) quasi-Monte Carlo (QMC) quadratures. The anchored decomposition allows us to compute $f_mathfrak{u}$ 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 $f_mathfrak{u}$ 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." @default.
- W4298380587 created "2022-10-02" @default.
- W4298380587 creator A5026757383 @default.
- W4298380587 creator A5045125806 @default.
- W4298380587 creator A5045896084 @default.
- W4298380587 creator A5071785514 @default.
- W4298380587 date "2017-12-19" @default.
- W4298380587 modified "2023-09-27" @default.
- W4298380587 title "Efficient implementations of the Multivariate Decomposition Method for approximating infinite-variate integrals" @default.
- W4298380587 doi "https://doi.org/10.48550/arxiv.1712.06782" @default.
- W4298380587 hasPublicationYear "2017" @default.
- W4298380587 type Work @default.
- W4298380587 citedByCount "0" @default.
- W4298380587 crossrefType "posted-content" @default.
- W4298380587 hasAuthorship W4298380587A5026757383 @default.
- W4298380587 hasAuthorship W4298380587A5045125806 @default.
- W4298380587 hasAuthorship W4298380587A5045896084 @default.
- W4298380587 hasAuthorship W4298380587A5071785514 @default.
- W4298380587 hasBestOaLocation W42983805871 @default.
- W4298380587 hasConcept C105795698 @default.
- W4298380587 hasConcept C11413529 @default.
- W4298380587 hasConcept C118615104 @default.
- W4298380587 hasConcept C120665830 @default.
- W4298380587 hasConcept C121332964 @default.
- W4298380587 hasConcept C122123141 @default.
- W4298380587 hasConcept C124681953 @default.
- W4298380587 hasConcept C134306372 @default.
- W4298380587 hasConcept C14036430 @default.
- W4298380587 hasConcept C141547133 @default.
- W4298380587 hasConcept C161584116 @default.
- W4298380587 hasConcept C167196314 @default.
- W4298380587 hasConcept C177264268 @default.
- W4298380587 hasConcept C18903297 @default.
- W4298380587 hasConcept C19499675 @default.
- W4298380587 hasConcept C199360897 @default.
- W4298380587 hasConcept C27016315 @default.
- W4298380587 hasConcept C28826006 @default.
- W4298380587 hasConcept C33923547 @default.
- W4298380587 hasConcept C41008148 @default.
- W4298380587 hasConcept C48265008 @default.
- W4298380587 hasConcept C62869609 @default.
- W4298380587 hasConcept C78458016 @default.
- W4298380587 hasConcept C86803240 @default.
- W4298380587 hasConceptScore W4298380587C105795698 @default.
- W4298380587 hasConceptScore W4298380587C11413529 @default.
- W4298380587 hasConceptScore W4298380587C118615104 @default.
- W4298380587 hasConceptScore W4298380587C120665830 @default.
- W4298380587 hasConceptScore W4298380587C121332964 @default.
- W4298380587 hasConceptScore W4298380587C122123141 @default.
- W4298380587 hasConceptScore W4298380587C124681953 @default.
- W4298380587 hasConceptScore W4298380587C134306372 @default.
- W4298380587 hasConceptScore W4298380587C14036430 @default.
- W4298380587 hasConceptScore W4298380587C141547133 @default.
- W4298380587 hasConceptScore W4298380587C161584116 @default.
- W4298380587 hasConceptScore W4298380587C167196314 @default.
- W4298380587 hasConceptScore W4298380587C177264268 @default.
- W4298380587 hasConceptScore W4298380587C18903297 @default.
- W4298380587 hasConceptScore W4298380587C19499675 @default.
- W4298380587 hasConceptScore W4298380587C199360897 @default.
- W4298380587 hasConceptScore W4298380587C27016315 @default.
- W4298380587 hasConceptScore W4298380587C28826006 @default.
- W4298380587 hasConceptScore W4298380587C33923547 @default.
- W4298380587 hasConceptScore W4298380587C41008148 @default.
- W4298380587 hasConceptScore W4298380587C48265008 @default.
- W4298380587 hasConceptScore W4298380587C62869609 @default.
- W4298380587 hasConceptScore W4298380587C78458016 @default.
- W4298380587 hasConceptScore W4298380587C86803240 @default.
- W4298380587 hasLocation W42983805871 @default.
- W4298380587 hasOpenAccess W4298380587 @default.
- W4298380587 hasPrimaryLocation W42983805871 @default.
- W4298380587 hasRelatedWork W1843732975 @default.
- W4298380587 hasRelatedWork W1963523105 @default.
- W4298380587 hasRelatedWork W1989863738 @default.
- W4298380587 hasRelatedWork W2003779866 @default.
- W4298380587 hasRelatedWork W2129704733 @default.
- W4298380587 hasRelatedWork W2180665983 @default.
- W4298380587 hasRelatedWork W2263220200 @default.
- W4298380587 hasRelatedWork W2550855422 @default.
- W4298380587 hasRelatedWork W2563740288 @default.
- W4298380587 hasRelatedWork W2963494703 @default.
- W4298380587 isParatext "false" @default.
- W4298380587 isRetracted "false" @default.
- W4298380587 workType "article" @default.