{
  "abstract": "We develop a flux-matched Poisson iteration for solving generated Jacobian equations with second boundary conditions. In each step, it solves a fixed shifted Poisson problem with a Neumann-type boundary condition. Near a smooth regular solution with positive $C^{1,1}$ densities, we prove that the iteration has local geometric convergence in $C^{2,α}$ on smooth connected Riemannian domains. The iteration is then discretized using a spectral Galerkin method, with local convergence proved for the Fourier-Jacobi scheme on spherical caps. Optical numerical experiments support these estimates and demonstrate useful imaging performance beyond the local convergence theory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06153",
  "author_total": 2,
  "authors": [
    {
      "name": "Haoxiang Zhang"
    },
    {
      "name": "Yixuan Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1rfvqwgqp6tc1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06153",
  "fulltext_url": null,
  "id": "1rfvqwgqp6tc1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06153",
  "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.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06153",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1rfvqwgqp6tc1.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06153",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06153"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Flux-Matched Poisson Iteration for Generated Jacobian Equations: Local Convergence and Spectral Galerkin Approximation",
  "title_text": "Flux-Matched Poisson Iteration for Generated Jacobian Equations: Local Convergence and Spectral Galerkin Approximation",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:30Z",
  "url": "https://research.draconitic.com/paper/1rfvqwgqp6tc1",
  "venue": "arXiv",
  "versions": []
}