Griebel, MichaelMichaelGriebelHamaekers, JanJanHamaekers2023-01-242023-01-242021-10-22https://publica.fraunhofer.de/handle/publica/43430410.1007/978-3-030-81362-8_3In (Griebel and Hamaekers, Fast discrete Fourier transform on generalized sparse grids, Sparse grids and Applications, volume 97 of Lecture Notes in Computational Science and Engineering, pages 75-108, Springer, 2014), an algorithm for trigonometric interpolation involving only so-called standard information of multivariate functions on generalized sparse grids has been suggested and a study on its application for the interpolation of functions in periodic Sobolev spaces of dominating mixed smoothness has been presented. In this complementary paper, we now give a slight modification of the proofs, which yields an extension from the pairing (Hs,Htmix) to the more general pairing (Hs,Ht,rmix) and which in addition results in an improved estimate for the interpolation error. The improved (constructive) upper bound is in particular consistent with the lower bound for sampling on regular sparse grids with r = 0 and s = 0 given in (Dũng, Acta Mathematica Vietnamica, 43(1):83-110, 2018; Dũng et al., Hyperbolic Cross Approximation, Advanced Courses in Mathematics - CRM Barcelona, Birkhäuser/Springer, 2018).enconference paper