An equi-directional generalization of adaptive cross approximation for higher-order tensors

A scheme for the equi-directional approximation of third-order tensors by sums of products of vectors is presented and analyzed. The new method is a generalization of the adaptive cross approximation (ACA) method initially designed for the low-rank approximation of matrices using only few of its original entries. Moreover, a recursive formula is presented which generalizes the three-way ACA to tensors of arbitrary order.