A note on rank constrained solutions to linear matrix equations
For researchers working on linear matrix equations, this is an incremental heuristic without theoretical guarantees.
The paper proposes a heuristic for finding rank-constrained solutions to linear matrix equations by minimizing a non-convex quadratic functional (Low-Rank-Functional). The method lacks formal proof but performs well in simulations with many numerical examples.
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.