{
  "abstract": "We present a preconditioning pipeline that accelerates Tensor Train (TT) linear solvers for symmetric positive-definite problems. Extending the Factorized Sparse Approximate Inverse framework to tensor networks, we construct a preconditioner as the product of a TT operator and its transpose. This formulation is positive semidefinite for any bond dimension and truncation, and definite whenever the factor is non-singular, satisfying the mathematical requirements of the Conjugate Gradient method. We detail the construction of this preconditioner and its integration into Density Matrix Renormalization Group (DMRG)-like linear solvers. Performance evaluations show consistent iteration reductions for anisotropic diffusion and Poisson problems across various configurations, leading to net speedups of up to 25% in ill-conditioned settings of time stepping schemes that can reuse the approximate inverses. These benchmarks were performed with the open-source Julia library DifferenTT.jl, which we also introduce in this work to provide out-of-the-box access to these preconditioned pipelines.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03859",
  "author_total": 4,
  "authors": [
    {
      "name": "Pau Torrente Badia"
    },
    {
      "name": "Daniel Pérez García"
    },
    {
      "name": "Artur Garcia-Saez"
    },
    {
      "name": "Stefano Carignano"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ex65zmgpacfea.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03859",
  "fulltext_url": null,
  "id": "ex65zmgpacfea",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03859",
  "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",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03859",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ex65zmgpacfea.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:25Z",
      "native_id": "2611.03859",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03859"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Factorized approximate inverse preconditioners in the tensor train format",
  "title_text": "Factorized approximate inverse preconditioners in the tensor train format",
  "type": "preprint",
  "updated_at": "2026-11-04T15:21:29Z",
  "url": "https://research.draconitic.com/paper/ex65zmgpacfea",
  "venue": "arXiv",
  "versions": []
}