Approximation of Two-variate Functions : Singular Value Decomposition versus Regular Sparse Grids

@inproceedings{Griebel2010ApproximationOT,
  title={Approximation of Two-variate Functions : Singular Value Decomposition versus Regular Sparse Grids},
  author={Michael Griebel and Helmut Harbrecht},
  year={2010}
}
We compare the cost complexities of two approximation schemes for functions f ∈ H(Ω1×Ω2) which live on the product domain Ω1 × Ω2 of general domains Ω1 ⊂ R1 and Ω2 ⊂ R2 , namely the singular value / Karhunen-Lòeve decomposition and the regular sparse grid representation. Here we assume that suitable finite element methods with associated fixed order r of accuracy are given on the domains Ω1 and Ω2. Then, the sparse grid approximation essentially needs only O(ε−max{n,n} r ) unknowns to reach a… CONTINUE READING

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