{
  "annotation_id": "5516e0e4-4a29-45e3-a7da-9f55cea0e02e",
  "date_created": "2026-03-02T18:01:21.479000Z",
  "date_modified": "2026-03-02T18:01:21.479000Z",
  "file_hash": "43c96b33d5cd812d3bd3809f6c991b3fb98ae99ec2100462dc00b39f2683ab04",
  "private": false,
  "record": {
    "abstract": "We present a comparative study of the application of modern eigenvalue\nalgorithms to an eigenvalue problem arising in quantum physics, namely, the\ncomputation of a few interior eigenvalues and their associated eigenvectors for\nthe large, sparse, real, symmetric, and indefinite matrices of the Anderson\nmodel of localization. We compare the Lanczos algorithm in the 1987\nimplementation of Cullum and Willoughby with the implicitly restarted Arnoldi\nmethod coupled with polynomial and several shift-and-invert convergence\naccelerators as well as with a sparse hybrid tridiagonalization method. We\ndemonstrate that for our problem the Lanczos implementation is faster and more\nmemory efficient than the other approaches. This seemingly innocuous problem\npresents a major challenge for all modern eigenvalue algorithms.",
    "arxiv_id": "physics/9802009",
    "authors": [
      "U. Elsner",
      "V. Mehrmann",
      "F. Milde",
      "R. A. Roemer",
      "M. Schreiber"
    ],
    "categories": [
      "physics.comp-ph"
    ],
    "doi": "10.1137/S1064827598332217",
    "journal_ref": "SIAM Journal on Scientific Computing, 20(6), 2089-2102 (1999)",
    "title": "The Anderson model of localization: a challenge for modern eigenvalue   methods",
    "url": "https://arxiv.org/abs/physics/9802009"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "0b34276d-f6ae-486d-b0ac-f2b3f34351d9",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}