{"paper":{"title":"Randomized Estimation of T-Eigenvalues of T-SPD Tensors: A Two-Sided Bracket","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Hemant Sharma, Nachiketa Mishra","submitted_at":"2026-06-23T12:24:13Z","abstract_excerpt":"In earlier work \\cite{sharma2025} we developed deterministic analytical bounds on the T-eigenvalues of symmetric positive definite (SPD) third-order tensors under the Kilmer--Martin T-product: the trace--determinant (TDet) bounds via the AM--GM inequality, and the trace-dependent (TDep) bounds generalizing Samuelson's inequality. While these bounds are cheap and guaranteed-valid, their relative gap grows as $\\sqrt{d-1}$ in the tensor dimension $d = np$, limiting their usefulness for large tensors.\n  This paper develops randomized estimators for the extreme T-eigenvalues of T-SPD tensors that c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.24491","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.24491/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}