{"paper":{"title":"Perturbation Analysis of An Eigenvector-Dependent Nonlinear Eigenvalue Problem With Applications?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Yunfeng Cai, Zheng-Jian Bai, Zhigang Jia","submitted_at":"2018-03-05T07:00:30Z","abstract_excerpt":"The eigenvector-dependent nonlinear eigenvalue problem (NEPv) $A(P)V=V\\Lambda$, where the columns of $V\\in\\mathbb{C}^{n\\times k}$ are orthonormal, $P=VV^{\\mathrm{H}}$, $A(P)$ is Hermitian, and $\\Lambda=V^{\\mathrm{H}}A(P)V$, arises in many important applications, such as the discretized Kohn-Sham equation in electronic structure calculations and the trace ratio problem in linear discriminant analysis. In this paper, we perform a perturbation analysis for the NEPv, which gives upper bounds for the distance between the solution to the original NEPv and the solution to the perturbed NEPv. A condit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.01518","kind":"arxiv","version":1},"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"}