{"paper":{"title":"An unconstrained optimization approach for finding real eigenvalues of even order symmetric tensors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Lixing Han","submitted_at":"2012-03-23T01:38:20Z","abstract_excerpt":"Let $n$ be a positive integer and $m$ be a positive even integer. Let ${\\mathcal A}$ be an $m^{th}$ order $n$-dimensional real weakly symmetric tensor and ${\\mathcal B}$ be a real weakly symmetric positive definite tensor of the same size. $\\lambda \\in R$ is called a ${\\mathcal B}_r$-eigenvalue of ${\\mathcal A}$ if ${\\mathcal A} x^{m-1} = \\lambda {\\mathcal B} x^{m-1}$ for some $x \\in R^n \\backslash \\{0\\}$. In this paper, we introduce two unconstrained optimization problems and obtain some variational characterizations for the minimum and maximum ${\\mathcal B}_r$--eigenvalues of ${\\mathcal A}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.5150","kind":"arxiv","version":5},"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"}