{
  "id": "2309.06331",
  "version": "v1",
  "published": "2023-09-12T15:42:50.000Z",
  "updated": "2023-09-12T15:42:50.000Z",
  "title": "Additive Stability of Frames",
  "authors": [
    "Oleg Asipchuk",
    "Jacob Glidewell",
    "Luis Rodriguez"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Given a frame in a finite dimensional Hilbert space we construct additive perturbations which decrease the condition number of the frame. By iterating this perturbation, we introduce an algorithm that produces a tight frame in a finite number of steps. Additionally, we give sharp bounds on additive perturbations which preserve frames and we study the effect of appending and erasing vectors to a given tight frame. We also discuss under which conditions our finite-dimensional results are extendable to infinite-dimensional Hilbert spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-12T15:42:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C15"
    ],
    "keywords": [
      "additive stability",
      "tight frame",
      "finite dimensional hilbert space",
      "infinite-dimensional hilbert spaces",
      "construct additive perturbations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}