423	RWTH Publication No: 478516        2015        IGPM423.pdf
TITLE	On the Convergence of Alternating Least Squares Optimisation in Tensor Format Representations
AUTHORS	Mike Espig, Wolfgang Hackbusch, Aram Khachatryan
ABSTRACT	The approximation of tensors is important for the efficient numerical treatment of high dimensional problems, but it remains an extremely challenging task. One of the most popular approach to tensor approximation is the alternating least squares method. In our study, the convergence of the alternating least squares algorithm is considered. The analysis is done for arbitrary tensor format representations and based on the multiliearity of the tensor format. In tensor format representation techniques, tensors are approximated by multilinear combinations of objects lower dimensionality. The resulting reduction of dimensionality not only reduces the amount of required storage but also the computational effort.
KEYWORDS	tensor format, tensor representation, tensor network, alternating least squares optimisation, orthogonal projection method