Error analysis for function representation by the sparse-grid combination technique
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.