{
  "abstract": "The performance of stationary iterative methods is memory-bound, due to the low arithmetic intensity. So, we propose a mixed-precision technique to reduce the amount of data movement in matrix-splitting iterative methods. We demonstrate both theoretically and experimentally that this technique will generally converge at a similar rate as an exact-precision iteration, depending on the precision used and the conditioning of the $M$ matrix. Furthermore, we demonstrate that iterative refinement can be used to refine the solution to full double-precision accuracy. Using this approach, we mixed half and double precision to achieve an average speedup over uniform double precision of $1.60\\times$ for scalar and block Jacobi and $1.25\\times$ for scalar and block Gauss-Seidel. Furthermore, we reduced the precision in the SSOR iteration used by OVERFLOW, a NASA code for compressible fluid dynamics simulations, and achieved a $1.14\\times$ speedup to the overall application.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06414",
  "author_total": 4,
  "authors": [
    {
      "name": "Neil Lindquist"
    },
    {
      "name": "David Appelhans"
    },
    {
      "name": "Chales W. Jackson"
    },
    {
      "name": "Joseph M. Derlaga"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/daakyrdvxrc6q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06414",
  "fulltext_url": null,
  "id": "daakyrdvxrc6q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06414",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CE"
    ],
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "1703|Matrix Theory and Algorithms"
    ]
  ],
  "openalex": "W7220737887",
  "pdf_url": "https://arxiv.org/pdf/2610.06414",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/daakyrdvxrc6q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.06414",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06414"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A Mixed-Precision Model for Matrix-Splitting Methods",
  "title_text": "A Mixed-Precision Model for Matrix-Splitting Methods",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/daakyrdvxrc6q",
  "venue": "arXiv",
  "versions": []
}