{
  "annotation_id": "471a1768-6d12-41c6-b3f6-9c6f3a0cc6e9",
  "date_created": "2026-03-02T18:01:03.865000Z",
  "date_modified": "2026-03-02T18:01:03.865000Z",
  "file_hash": "3f92c1bf01b3e485f15f9874406a1cb4273e5c407f44baca4570df17ee491537",
  "private": false,
  "record": {
    "abstract": "An alternative to the matrix inverse procedure is presented. Given a bit\nregister which is arbitrarily large, the matrix inverse to an arbitrarily large\nmatrix can be peformed in ${\\cal O}(N^2)$ operations, and to matrix\nmultiplication on a vector in ${\\cal O}(N)$. This is in contrast to the usual\n${\\cal O}(N^3)$ and ${\\cal O}(N^2)$. A finite size bit register can lead to\nspeeds up of an order of magnitude in large matrices such as $500\\times 500$.\nThe FFT can be improved from ${\\cal O}(N\\ln N)$ to ${\\cal O}(N)$ steps, or even\nfewer steps in a modified butterfly configuration.",
    "arxiv_id": "physics/0601134",
    "authors": [
      "Gordon Chalmers"
    ],
    "categories": [
      "physics.gen-ph"
    ],
    "title": "Computational Improvements to Matrix Operations",
    "url": "https://arxiv.org/abs/physics/0601134"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "fad05e55-e1f5-4d47-b97d-aa78dc87f5f5",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}