{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:VMOPMW3BVPAVJ2G42PFVYU5INE","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ec0bd120fa4b17dec69df57a2f5e0eed461ae258d9518623a387f451bdc5b7a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-06-12T01:20:36Z","title_canon_sha256":"ea30ca719df5c3306c5cf4e12e011830239f63739a3fa36f8d9b3dbd2328d84d"},"schema_version":"1.0","source":{"id":"0906.2238","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.2238","created_at":"2026-05-18T03:52:39Z"},{"alias_kind":"arxiv_version","alias_value":"0906.2238v3","created_at":"2026-05-18T03:52:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.2238","created_at":"2026-05-18T03:52:39Z"},{"alias_kind":"pith_short_12","alias_value":"VMOPMW3BVPAV","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"VMOPMW3BVPAVJ2G4","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"VMOPMW3B","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:4ee4c3e0ecbcdb08340e8407baa2b0e51d8bf5cfe258ffef1fb6ac90e068d882","target":"graph","created_at":"2026-05-18T03:52:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"For the Hermitian inexact Rayleigh quotient iteration (RQI), we present a new general theory, independent of iterative solvers for shifted inner linear systems. The theory shows that the method converges at least quadratically under a new condition, called the uniform positiveness condition, that may allow inner tolerance $\\xi_k\\geq 1$ at outer iteration $k$ and can be considerably weaker than the condition $\\xi_k\\leq\\xi<1$ with $\\xi$ a constant not near one commonly used in literature. We consider the convergence of the inexact RQI with the unpreconditioned and tuned preconditioned MINRES met","authors_text":"Zhongxiao Jia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-06-12T01:20:36Z","title":"On Convergence of the Inexact Rayleigh Quotient Iteration with MINRES"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.2238","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:bc57774cf0ad57b13f1e118c7d1e48d7ce890022a34497d542a644f86db9e43b","target":"record","created_at":"2026-05-18T03:52:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ec0bd120fa4b17dec69df57a2f5e0eed461ae258d9518623a387f451bdc5b7a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-06-12T01:20:36Z","title_canon_sha256":"ea30ca719df5c3306c5cf4e12e011830239f63739a3fa36f8d9b3dbd2328d84d"},"schema_version":"1.0","source":{"id":"0906.2238","kind":"arxiv","version":3}},"canonical_sha256":"ab1cf65b61abc154e8dcd3cb5c53a86931822bb19d0638ec81bfed569f51243e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab1cf65b61abc154e8dcd3cb5c53a86931822bb19d0638ec81bfed569f51243e","first_computed_at":"2026-05-18T03:52:39.001745Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:52:39.001745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BUBK41AFYljlxVgaZqLbnQS9dq5QFvBmp0DYEVhlziApgDxBFTg8qfi8J/xQPLgMgj/CAGRFw1V8b7EmzjkoDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:52:39.002348Z","signed_message":"canonical_sha256_bytes"},"source_id":"0906.2238","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc57774cf0ad57b13f1e118c7d1e48d7ce890022a34497d542a644f86db9e43b","sha256:4ee4c3e0ecbcdb08340e8407baa2b0e51d8bf5cfe258ffef1fb6ac90e068d882"],"state_sha256":"9774c55323852c5ee9d6ad1756b455861216d67a633036e7ab8d5fcd45ce32a8"}