A note on rank constrained solutions to linear matrix equations
Optimization and Control
2018-09-10 v1 Systems and Control
Abstract
This preliminary note presents a heuristic for determining rank constrained solutions to linear matrix equations (LME). The method proposed here is based on minimizing a non-convex quadratic functional, which will hence-forth be termed as the \textit{Low-Rank-Functional} (LRF). Although this method lacks a formal proof/comprehensive analysis, for example in terms of a probabilistic guarantee for converging to a solution, the proposed idea is intuitive and has been seen to perform well in simulations. To that end, many numerical examples are provided to corroborate the idea.
Cite
@article{arxiv.1809.02491,
title = {A note on rank constrained solutions to linear matrix equations},
author = {Shravan Mohan},
journal= {arXiv preprint arXiv:1809.02491},
year = {2018}
}