, Volume 71, Issue 1, pp 89–114 | Cite as

Multivariate Quadrature on Adaptive Sparse Grids

  • H.-J. BungartzEmail author
  • S. Dirnstorfer


In this paper, we study the potential of adaptive sparse grids for multivariate numerical quadrature in the moderate or high dimensional case, i. e. for a number of dimensions beyond three and up to several hundreds. There, conventional methods typically suffer from the curse of dimension or are unsatisfactory with respect to accuracy. Our sparse grid approach, based upon a direct higher order discretization on the sparse grid, overcomes this dilemma to some extent, and introduces additional flexibility with respect to both the order of the 1 D quadrature rule applied (in the sense of Smolyak's tensor product decomposition) and the placement of grid points. The presented algorithm is applied to some test problems and compared with other existing methods.

AMS Subject Classification

65D30 65D32 65Y20 


multivariate numerical quadrature sparse grids higher order adaptivity 


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Copyright information

© Springer-Verlag Wien 2003

Authors and Affiliations

  1. 1.IPVS, Universität StuttgartUniversitätsstraßeStuttgartGermany
  2. 2.Nagler & CompanySchnaittenbachGermany

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