TECHNISCHE UNIVERSITÄT BERLIN On best rank one approximation of tensors

Technische Universität Berlin Institut für Mathematik Fundamental Diagrams and Multiple Pedestrian Streams

Technische Universität Berlin Institut für Mathematik Some Fundamental Considerations for the Application of Macroscopic Models in the Field of Pedestrian Crowd Simulation

Orthogonal Rank-two Tensor Approximation: a Modified High-order Power Method and Its Convergence Analysis

With the notable exceptions that tensors of order 2, that is, matrices always have best approximations of arbitrary low ranks and that tensors of any order always have the best rank-one approximation, it is known that high-order tensors can fail to have best low rank approximations. When the condition of orthogonality is imposed, even at the most general case that only one pair of components in...

Orthogonal Low Rank Tensor Approximation: Alternating Least Squares Method and Its Global Convergence

With the notable exceptions of two cases — that tensors of order 2, namely, matrices, always have best approximations of arbitrary low ranks and that tensors of any order always have the best rank-one approximation, it is known that high-order tensors may fail to have best low rank approximations. When the condition of orthogonality is imposed, even under the modest assumption that only one set...

Best Rank-One Tensor Approximation and Parallel Update Algorithm for CPD

A novel algorithm is proposed for CANDECOMP/PARAFAC tensor decomposition to exploit best rank-1 tensor approximation. Different from the existing algorithms, our algorithm updates rank-1 tensors simultaneously in-parallel. In order to achieve this, we develop new all-at-once algorithms for best rank-1 tensor approximation based on the Levenberg-Marquardt method and the rotational update. We sho...