{
  "abstract": "A relaxed shifted matrix-splitting modulus-based iteration method is proposed for solving large-scale sparse linear complementarity problems. The method extends the classical modulus-based matrix-splitting framework by introducing two shift parameters into the matrix splitting while preserving the original coefficient matrix. Different choices of the splitting lead to shifted Jacobi, Gauss-Seidel, SOR, and AOR-type schemes. Sufficient convergence conditions are established for \\(P\\)-matrices and \\(H_+\\)-matrices. For structured sparse matrices, practical AOR-type conditions and explicit admissible intervals for the shift parameters are also derived. These intervals are used together with a grid-search procedure to select efficient parameter pairs. Numerical experiments on four large-scale sparse test problems, including a quasi-variational inequality model, show that the proposed method is competitive with several existing modulus-based and projected methods. A direct comparison with the two-parameter MAOR method further illustrates the effect of the proposed shifted splitting.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11949",
  "author_total": 3,
  "authors": [
    {
      "name": "Abhishek Kumar Singh Sengar"
    },
    {
      "name": "Bharat Kumar"
    },
    {
      "name": "Deepmala"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a64y3vb84a4gr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11949",
  "fulltext_url": null,
  "id": "a64y3vb84a4gr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11949",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
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      "arxiv",
      "math.NA"
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      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1703|Matrix Theory and Algorithms"
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  "openalex": "W7212560413",
  "pdf_url": "https://arxiv.org/pdf/2609.11949",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a64y3vb84a4gr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.11949",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11949"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Solving Large-Scale Sparse Linear Complementarity Problems Using a Relaxed Shifted Matrix-Splitting Modulus-Based Iteration Method",
  "title_text": "Solving Large-Scale Sparse Linear Complementarity Problems Using a Relaxed Shifted Matrix-Splitting Modulus-Based Iteration Method",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/a64y3vb84a4gr",
  "venue": "arXiv",
  "versions": []
}