Beschreibung:
In this article we introduce a black box type approximation algorithm for tensors A in high dimension d. The algorithm determines adaptively the positions of entries of the tensor that have to be computed or read, and using these (few) entries it constructs a low rank tensor approximation X that minimizes the l2-distance between A and X at the chosen positions. The full tensor A is not required, only the evaluation of A at a few positions. The minimization problem is solved by Newton's method which requires the computation and evaluation of the Hessian. For efficiency reasons the positions are located on fibre-crosses of the tensor so that the Hessian can be assembled and evaluated in a data-sparse form requiring a complexity of O(Pd), where P is the number of fibre-crosses and d the order of the tensor.