{
  "abstract": "We present an adaptive bitwidth allocation method for quantizing low-rank factors in hierarchical matrices in order to decrease storage while meeting a given constraint on their reconstruction error. For the bitwidth allocation we formulate a discrete storage minimization problem and show that an optimal assignment can give larger singular values at least as many bits as smaller ones. We further develop a greedy algorithm that meets the specified max-norm quantization error budget. We investigate a hierarchical block partition in which all of the non-diagonal blocks are represented by quantized low-rank factors and only dense blocks remain dense; in this way a global reconstruction bound related to $η_k$ and $R_k$ is obtained, with the former and latter being bounds on the truncation and reconstruction arithmetic errors, respectively. Extensive simulations, carried out with kernel and BEM matrices under block-relative budgets, indicate that the proposed method achieves a reduction in storage of up to $44.3\\times$ when compared to storing the complete matrix densely in FP64, and a reduction of up to $5.70\\times$ when compared to the FP64 low-rank factors within the same partition, together with measured reconstruction errors that remained below the maximum norm bounds in all the hierarchical tests.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40134",
  "author_total": 3,
  "authors": [
    {
      "name": "Erin Carson"
    },
    {
      "name": "Xinye Chen"
    },
    {
      "name": "Ritesh Khan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/042zdn1v04ycv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40134",
  "fulltext_url": null,
  "id": "042zdn1v04ycv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40134",
  "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.MS"
    ],
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "cs.PF"
    ],
    [
      "arxiv",
      "math.NA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40134",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/042zdn1v04ycv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.40134",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40134"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Integer-Quantized Hierarchical Matrices with Adaptive Bit Allocation",
  "title_text": "Integer-Quantized Hierarchical Matrices with Adaptive Bit Allocation",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/042zdn1v04ycv",
  "venue": "arXiv",
  "versions": []
}