  We present an iterative method for the search of extreme entries in low-rank
tensors which is based on a power iteration combined with a binary search. In
this work we use the HT-format for low-rank tensors but other low-rank formats
can be used verbatim. We present two different approaches to accelerate the
basic power iteration: an orthogonal projection of Rayleigh-Ritz type, as well
as an acceleration of the power iteration itself which can be achieved due to
the diagonal structure of the underlying eigenvalue problem. Finally the
maximizing index is determined by a binary search based on the proposed
iterative method for the approximation of the maximum norm. The iterative
method for the maximum norm estimation inherits the linear complexity of the
involved tensor arithmetic in the HT-format w.r.t. the tensor order, which is
also verified by numerical tests.
