{"paper":{"title":"Solution of the $k$-th eigenvalue problem in large-scale electronic structure calculations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Dongjin Lee, Shao-Liang Zhang, Takeo Hoshi, Tomohiro Sogabe, Yuto Miyatake","submitted_at":"2017-10-14T05:19:34Z","abstract_excerpt":"We consider computing the $k$-th eigenvalue and its corresponding eigenvector of a generalized Hermitian eigenvalue problem of $n\\times n$ large sparse matrices. In electronic structure calculations, several properties of materials, such as those of optoelectronic device materials, are governed by the eigenpair with a material-specific index $k.$ We present a three-stage algorithm for computing the $k$-th eigenpair with validation of its index. In the first stage of the algorithm, we propose an efficient way of finding an interval containing the $k$-th eigenvalue $(1 \\ll k \\ll n)$ with a non-s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05134","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}