{
  "abstract": "The generalized Fisher transformation maps a non-singular correlation matrix to an unconstrained real vector through the off-diagonal elements of its matrix logarithm. Evaluating its inverse is a computational bottleneck in dynamic correlation and multivariate volatility models. We develop a fast inversion algorithm by characterizing the unknown diagonal as the minimizer of a smooth, strictly convex, and coercive objective. An explicit Hessian and global spectral bounds identify the standard fixed-point iteration as a quasi-Newton method and explain why it can converge slowly near singularity. Every fixed-point step decreases the objective, and the iteration converges from every starting point. These results motivate GFT-FP+N, a hybrid of fixed-point and matrix-free Newton steps that never forms the Jacobian. In benchmarks with up to 1,000 replications per design and dimensions up to 800, GFT-FP+N reduces computation time by up to a factor of forty-five relative to the fixed-point iteration and converged in every replication, including on designs where Broyden's method almost always fails. Julia and R packages are provided.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19028",
  "author_total": 2,
  "authors": [
    {
      "name": "Ilya Archakov"
    },
    {
      "name": "Peter Reinhard Hansen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/71v1y09xrnb0b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19028",
  "fulltext_url": null,
  "id": "71v1y09xrnb0b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19028",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "econ.EM"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.CO"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "1703|Matrix Theory and Algorithms"
    ]
  ],
  "openalex": "W7213519618",
  "pdf_url": "https://arxiv.org/pdf/2609.19028",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/71v1y09xrnb0b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.19028",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19028"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Fast inversion of the generalized Fisher transformation of correlation matrices",
  "title_text": "Fast inversion of the generalized Fisher transformation of correlation matrices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:49Z",
  "url": "https://research.draconitic.com/paper/71v1y09xrnb0b",
  "venue": "arXiv",
  "versions": []
}