{
  "id": "1809.02491",
  "version": "v1",
  "published": "2018-09-06T06:18:22.000Z",
  "updated": "2018-09-06T06:18:22.000Z",
  "title": "A note on rank constrained solutions to linear matrix equations",
  "authors": [
    "Shravan Mohan"
  ],
  "categories": [
    "math.OC",
    "cs.SY"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-06T06:18:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "linear matrix equations",
      "non-convex quadratic functional",
      "probabilistic guarantee",
      "determining rank constrained solutions",
      "formal proof/comprehensive analysis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}