In this paper, we give a unified approach to error estimates for interpolation on sparse Gauss--Chebyshev grids for multivariate functions from Besov--type spaces with dominating mixed smoothness properties. The error bounds obtained for this method are almost optimal for the considered scale of function spaces.

Interpolation (msc 41A05), Multidimensional problems (should also be assigned at least one other classification number in this section) (msc 41A63), Interpolation (msc 65D05), Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems (msc 46E35)
Modelling, Analysis and Simulation [MAS]

Sprengel, F. (1998). Interpolation on sparse Gauss-Chebyshev grids in higher dimensions. Modelling, Analysis and Simulation [MAS]. CWI.