Generalized cross approximation for 3d-tensors

In this article we present a generalized version of the Cross Approximation for 3d-ten-sors. The given tensor a ∈ R n×n×n is represented as a matrix of vectors and 2d adaptive Cross Approximation is applied in a nested way to get the tensor decomposition. The main focus lies on theoretical issues of the construction such as the desired interpolation property or the explicit formulas for the vectors in the decomposition. The computational complexity of the proposed algorithm is shown to be linear in n.