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@MISC{,
            author = {Dolgov, Sergey and Vejchodsk{\'{y}}, Tom{\'{a}}{\v s}},
             title = {Guaranteed a posteriori error bounds for low rank tensor approximate solutions},
              year = {2019},
          abstract = {We propose guaranteed and fully computable upper bound on the
energy norm of the error in low rank Tensor Train (TT) approximate
solutions of (possibly) high dimensional reaction-diusion problems.
The error bound is obtained from Euler{Lagrange equations for a complementary

ux reconstruction problem, which are solved in the low
rank TT representation using the block Alternating Linear Scheme.
This bound is guaranteed to be above the energy norm of the total error,
including the discretization error, the tensor approximation error,
and the error in the solver of linear algebraic equations. Numerical examples
with the Poisson equation and the Schrodinger equation with
the Henon-Heiles potential in up to 40 dimensions are presented to
illustrate the eciency of this approach.},
  Preprint project = {NCMM},
     Preprint year = {2019},
   Preprint number = {03},
       Preprint ID = {NCMM/2019/03}
}