{
  "abstract": "We propose a doubly inertial coupled dynamical system (DICDS) for linear inverse problems, extending an existing first-order coupled dynamical system by introducing second-order dynamics for both the unknown variable x and an auxiliary variable y representing the measurement process. Rather than designing an iterative algorithm directly, we formulate the problem as a continuous-time dynamical system whose equilibrium coincides with the solution set of the underlying model, and establish its asymptotic stability via a spectral analysis yielding a necessary and sufficient condition and a Lyapunov-function argument yielding a sufficient condition that clarifies the dissipative structure of the dynamics. This stability theory covers both underdetermined systems, where the equilibrium forms a manifold, and the complementary case with at least as many measurements as unknowns, where it reduces to a unique point whose x-component is the least-squares solution. A direct Euler discretization of the DICDS is numerically unstable; instead, we formulate a separate quasi-inertial continuous-time system that shares the same equilibrium structure and whose Euler discretization yields a two-variable iterative algorithm with momentum-type updates. Numerical experiments on tomographic reconstruction show that the proposed algorithm achieves more effective noise suppression and structural preservation than the corresponding non-inertial coupled method, with the coupling and inertial mechanisms playing distinct roles depending on the measurement-noise level.",
  "abstract_shown": true,
  "affiliations": [
    "Institute of Biomedical Sciences, Tokushima University, 3-18-15 Kuramoto, Tokushima 770-8509, Japan",
    "Faculty of Science, Tanta University, El-Giesh St., Tanta 31527, Egypt"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Ryosuke Kasai",
      "orcid": "0000-0002-4699-1642"
    },
    {
      "affs": [
        0
      ],
      "name": "Tetsuya Yoshinaga",
      "orcid": "0000-0003-4994-0522"
    },
    {
      "affs": [
        1
      ],
      "name": "Omar M. Abou Al-Ola",
      "orcid": "0000-0002-7883-676X"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b54kvp2n5ngj7.bib",
  "cited_by": 0,
  "doi": "10.3390/math14203713",
  "fulltext_url": null,
  "id": "b54kvp2n5ngj7",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/20/3713",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2610|Numerical methods in inverse problems"
    ]
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  "openalex": "W7221654545",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/b54kvp2n5ngj7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14203713",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/20/3713"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2610|Numerical methods in inverse problems",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Doubly Inertial Coupled Dynamical System for Linear Inverse Problems",
  "title_text": "Doubly Inertial Coupled Dynamical System for Linear Inverse Problems",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/b54kvp2n5ngj7",
  "venue": "Mathematics",
  "versions": []
}