Sparse grids, combined with gradient penalties provide an attractive tool for regularised least squares fitting. It has earlier been found that the combination technique, which build a sparse grid function using a linear combination of approximations on partial grids, is here not as effective as in the case of elliptic partial differential equations. The authors argue that this is due to the irregular and random data distribution, as well as the proportion of the number of data to the grid resolution. These effects are investigated both theoretically and by experiments.
Reviewer: Rózsa Horvàth-Bokor (Budapest)