{
  "id": "2204.03927",
  "version": "v1",
  "published": "2022-04-08T08:42:11.000Z",
  "updated": "2022-04-08T08:42:11.000Z",
  "title": "On computing the symplectic $LL^T$ factorization",
  "authors": [
    "Maksymilian Bujok",
    "Alicja Smoktunowicz",
    "Grzegorz Borowik"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "We analyze two algorithms for computing the symplectic $LL^T$ factorization $A=LL^T$ of a given symmetric positive definite symplectic matrix $A$. The first algorithm $W_1$ is an implementation of the $HH^T$ factorization from [Dopico et al., 2009], see Theorem 5.2. The second one, algorithm $W_2$ uses both Cholesky and Reverse Cholesky decompositions of symmetric positive definite matrices. We presents a comparison of these algorithms and illustrate their properties by numerical experiments in MATLAB. A particular emphasis is given on simplecticity properties of the computed matrices in floating-point arithmetic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-08T08:42:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15B10",
      "15B57",
      "65F25",
      "65F35"
    ],
    "keywords": [
      "factorization",
      "symmetric positive definite symplectic matrix",
      "reverse cholesky decompositions",
      "symmetric positive definite matrices",
      "first algorithm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}