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Sakurai,z-Pares: Parallel eigenvalue solver, 2014, https://zpares.cs. tsukuba.ac.jp/","work_id":"36205b18-2f0c-425d-9e00-0c102fe748ff","year":2014},{"cited_arxiv_id":"","doi":"10.1137/1.9781421407944","is_internal_anchor":false,"ref_index":5,"title":"Johns Hopkins University Press, Baltimore, MD (2013)","work_id":"56ab21a4-5482-4781-9604-cc0d1ed1c080","year":2013}],"snapshot_sha256":"8f4fadb0cf31aff1d5c62d5d287085ee6e0c50544f452f58ebec522c62118be8"},"source":{"id":"2605.12846","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-14T19:09:11.641218Z","id":"897b7c4f-7ed7-4804-a7fd-f0956b068d9f","model_set":{"reader":"grok-4.3"},"one_line_summary":"Refined SS-RRR methods with a reliable tune-free removal of spurious Ritz values improve accuracy and efficiency for computing eigenpairs of large Hermitian matrices in a target region.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Refined Rayleigh-Ritz projection enables tune-free removal of spurious Ritz values in Hermitian eigenproblems by exploiting unconditional convergence of refined vectors.","strongest_claim":"Exploiting the unconditional convergence of the refined Ritz vectors when the subspace is sufficiently accurate, we propose a tune-free removal approach to effectively remove spurious Ritz values with a rigorous theory supported, and develop a restarted CJ--SS--RRR algorithm. 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