Detailed error analyses are given for sparse-grid function representations through the combination technique. Two- and three-dimensional, and smooth and discontinuous functions are considered, as well as piecewise-constant and piecewise-linear interpolation techniques. Where appropriate, the results of the analyses are verified in numerical experiments. Instead of the common vertex-based function representation, cell-centered function representation is considered. Explicit, pointwise error expressions for the representation error are given, rather than order estimates. The paper contributes to the theory of sparse-grid techniques.

Series expansions (e.g. Taylor, Lidstone series, but not Fourier series) (msc 41A58), Interpolation (msc 65D05), None of the above, but in MSC2010 section 65Gxx (msc 65G99), Multigrid methods; domain decomposition (msc 65M55)
Life Sciences (theme 5), Energy (theme 4)
Modelling, Analysis and Simulation [MAS]
Scientific Computing

Lastdrager, B, & Koren, B. (1998). Error analysis for function representation by the sparse-grid combination technique. Modelling, Analysis and Simulation [MAS]. CWI.