Linear Systems with a Canonical Polyadic Decomposition Constrained Solution: Algorithms and Applications

© 2018 John Wiley & Sons, Ltd. Real-life data often exhibit some structure and/or sparsity, allowing one to use parsimonious models for compact representation and approximation. When considering matrix and tensor data, low-rank models such as the (multilinear) singular value decomposition, canonical polyadic decomposition (CPD), tensor train, and hierarchical Tucker model are very common. The solution of (large-scale) linear systems is often structured in a similar way, allowing one to use compact matrix and tensor models as well. In this paper, we focus on linear systems with a CPD-constrained solution (LS-CPD). Our main contribution is the development of optimization-based and algebraic methods to solve LS-CPDs. Furthermore, we propose a condition that guarantees generic uniqueness of the obtained solution. We also show that LS-CPDs provide a broad framework for the analysis of multilinear systems of equations. The latter are a higher-order generalization of linear systems, similar to tensor decompositions being a generalization of matrix decompositions. The wide applicability of LS-CPDs in domains such as classification, multilinear algebra, and signal processing is illustrated.status: publishe

Transportation of the Fission Fragments by the Gas Flow with Aerosol

The experimental setup for the transportation of the fission fragments by the gaseous flow with aerosols is described. The results of the setup testing using the {238}U photofission fragments are presented. The obtained parameters (transport efficiency up to 60 % and transport time down to 0.1 s at 1 m distance) allow one to use this setup in the experiments on the heavy nuclei fission and fragment properties investigation