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

Authors:
M. Bebendorf;A. Kühnemund;S. Rjasanow
Affiliations:
Institut für Numerische Simulation, Rheinische Friedrich-Wilhelms-Universität Bonn, Germany;Institut für Numerische Simulation, Rheinische Friedrich-Wilhelms-Universität Bonn, Germany;Fachbereich 6.1 - Mathematik, Universität des Saarlandes, Germany
Venue:
Applied Numerical Mathematics
Year:
2013

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Abstract

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.