Finding entries of maximum absolute value in low-rank tensors

Understand

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.