Numerical Optimization for Symmetric Tensor Decomposition
Numerical Analysis
2018-08-23 v2 Numerical Analysis
Abstract
We consider the problem of decomposing a real-valued symmetric tensor as the sum of outer products of real-valued vectors. Algebraic methods exist for computing complex-valued decompositions of symmetric tensors, but here we focus on real-valued decompositions, both unconstrained and nonnegative, for problems with low-rank structure. We discuss when solutions exist and how to formulate the mathematical program. Numerical results show the properties of the proposed formulations (including one that ignores symmetry) on a set of test problems and illustrate that these straightforward formulations can be effective even though the problem is nonconvex.
Cite
@article{arxiv.1410.4536,
title = {Numerical Optimization for Symmetric Tensor Decomposition},
author = {Tamara G. Kolda},
journal= {arXiv preprint arXiv:1410.4536},
year = {2018}
}