Matches in SemOpenAlex for { <https://semopenalex.org/work/W4317505528> ?p ?o ?g. }
- W4317505528 endingPage "534" @default.
- W4317505528 startingPage "534" @default.
- W4317505528 abstract "Numerical integration is a basic step in the implementation of more complex numerical algorithms suitable, for example, to solve ordinary and partial differential equations. The straightforward extension of a one-dimensional integration rule to a multidimensional grid by the tensor product of the spatial directions is deemed to be practically infeasible beyond a relatively small number of dimensions, e.g., three or four. In fact, the computational burden in terms of storage and floating point operations scales exponentially with the number of dimensions. This phenomenon is known as the curse of dimensionality and motivated the development of alternative methods such as the Monte Carlo method. The tensor product approach can be very effective for high-dimensional numerical integration if we can resort to an accurate low-rank tensor-train representation of the integrand function. In this work, we discuss this approach and present numerical evidence showing that it is very competitive with the Monte Carlo method in terms of accuracy and computational costs up to several hundredths of dimensions if the integrand function is regular enough and a sufficiently accurate low-rank approximation is available." @default.
- W4317505528 created "2023-01-20" @default.
- W4317505528 creator A5006188151 @default.
- W4317505528 creator A5007272760 @default.
- W4317505528 creator A5014223403 @default.
- W4317505528 creator A5038345001 @default.
- W4317505528 creator A5079029372 @default.
- W4317505528 date "2023-01-19" @default.
- W4317505528 modified "2023-09-25" @default.
- W4317505528 title "Challenging the Curse of Dimensionality in Multidimensional Numerical Integration by Using a Low-Rank Tensor-Train Format" @default.
- W4317505528 cites W1646309082 @default.
- W4317505528 cites W194074478 @default.
- W4317505528 cites W1954993463 @default.
- W4317505528 cites W1967859589 @default.
- W4317505528 cites W1975720704 @default.
- W4317505528 cites W1980906180 @default.
- W4317505528 cites W1988996307 @default.
- W4317505528 cites W1993482030 @default.
- W4317505528 cites W1998213879 @default.
- W4317505528 cites W2001518794 @default.
- W4317505528 cites W2004971474 @default.
- W4317505528 cites W2014945091 @default.
- W4317505528 cites W2023854932 @default.
- W4317505528 cites W2033022456 @default.
- W4317505528 cites W2081023708 @default.
- W4317505528 cites W2088025933 @default.
- W4317505528 cites W2117730583 @default.
- W4317505528 cites W2149381887 @default.
- W4317505528 cites W2149498546 @default.
- W4317505528 cites W2160346753 @default.
- W4317505528 cites W2168071446 @default.
- W4317505528 cites W2963363740 @default.
- W4317505528 cites W2969432895 @default.
- W4317505528 cites W3190382835 @default.
- W4317505528 cites W4205288342 @default.
- W4317505528 cites W4231866801 @default.
- W4317505528 cites W4239957396 @default.
- W4317505528 cites W4248057375 @default.
- W4317505528 cites W4288079944 @default.
- W4317505528 cites W50417968 @default.
- W4317505528 doi "https://doi.org/10.3390/math11030534" @default.
- W4317505528 hasPublicationYear "2023" @default.
- W4317505528 type Work @default.
- W4317505528 citedByCount "0" @default.
- W4317505528 crossrefType "journal-article" @default.
- W4317505528 hasAuthorship W4317505528A5006188151 @default.
- W4317505528 hasAuthorship W4317505528A5007272760 @default.
- W4317505528 hasAuthorship W4317505528A5014223403 @default.
- W4317505528 hasAuthorship W4317505528A5038345001 @default.
- W4317505528 hasAuthorship W4317505528A5079029372 @default.
- W4317505528 hasBestOaLocation W43175055281 @default.
- W4317505528 hasConcept C105795698 @default.
- W4317505528 hasConcept C111030470 @default.
- W4317505528 hasConcept C11413529 @default.
- W4317505528 hasConcept C114614502 @default.
- W4317505528 hasConcept C126255220 @default.
- W4317505528 hasConcept C127349201 @default.
- W4317505528 hasConcept C134306372 @default.
- W4317505528 hasConcept C14036430 @default.
- W4317505528 hasConcept C155281189 @default.
- W4317505528 hasConcept C164226766 @default.
- W4317505528 hasConcept C17744445 @default.
- W4317505528 hasConcept C19499675 @default.
- W4317505528 hasConcept C199539241 @default.
- W4317505528 hasConcept C202444582 @default.
- W4317505528 hasConcept C2524010 @default.
- W4317505528 hasConcept C2776359362 @default.
- W4317505528 hasConcept C28826006 @default.
- W4317505528 hasConcept C33923547 @default.
- W4317505528 hasConcept C41008148 @default.
- W4317505528 hasConcept C48753275 @default.
- W4317505528 hasConcept C51255310 @default.
- W4317505528 hasConcept C78458016 @default.
- W4317505528 hasConcept C86803240 @default.
- W4317505528 hasConcept C94625758 @default.
- W4317505528 hasConceptScore W4317505528C105795698 @default.
- W4317505528 hasConceptScore W4317505528C111030470 @default.
- W4317505528 hasConceptScore W4317505528C11413529 @default.
- W4317505528 hasConceptScore W4317505528C114614502 @default.
- W4317505528 hasConceptScore W4317505528C126255220 @default.
- W4317505528 hasConceptScore W4317505528C127349201 @default.
- W4317505528 hasConceptScore W4317505528C134306372 @default.
- W4317505528 hasConceptScore W4317505528C14036430 @default.
- W4317505528 hasConceptScore W4317505528C155281189 @default.
- W4317505528 hasConceptScore W4317505528C164226766 @default.
- W4317505528 hasConceptScore W4317505528C17744445 @default.
- W4317505528 hasConceptScore W4317505528C19499675 @default.
- W4317505528 hasConceptScore W4317505528C199539241 @default.
- W4317505528 hasConceptScore W4317505528C202444582 @default.
- W4317505528 hasConceptScore W4317505528C2524010 @default.
- W4317505528 hasConceptScore W4317505528C2776359362 @default.
- W4317505528 hasConceptScore W4317505528C28826006 @default.
- W4317505528 hasConceptScore W4317505528C33923547 @default.
- W4317505528 hasConceptScore W4317505528C41008148 @default.
- W4317505528 hasConceptScore W4317505528C48753275 @default.
- W4317505528 hasConceptScore W4317505528C51255310 @default.
- W4317505528 hasConceptScore W4317505528C78458016 @default.
- W4317505528 hasConceptScore W4317505528C86803240 @default.