Two-Level QTT-Tucker Format for Optimized Tensor Calculus

@article{Dolgov2013TwoLevelQF,
  title={Two-Level QTT-Tucker Format for Optimized Tensor Calculus},
  author={S. V. Dolgov and Boris N. Khoromskij},
  journal={SIAM J. Matrix Analysis Applications},
  year={2013},
  volume={34},
  pages={593-623}
}
We prove by counterexample that the bound on the rounding error given in Theorem 5.2 of [Dolgov and Khoromskij, SIAM J. Matrix Anal. Appl., 34 (2013), pp. 593–623] does not hold in general. A correct version of the error bound as well as a modified rounding algorithm for which the original bound holds are presented.