{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:J7D2YQ45EDIRA2XGHXGVG5G4XV","short_pith_number":"pith:J7D2YQ45","schema_version":"1.0","canonical_sha256":"4fc7ac439d20d1106ae63dcd5374dcbd51fc5bd1f7b8c199ff3fb485413497af","source":{"kind":"arxiv","id":"1206.1506","version":2},"attestation_state":"computed","paper":{"title":"A framework for deflated and augmented Krylov subspace methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Andr\\'e Gaul, J\\\"org Liesen, Martin H. Gutknecht, Reinhard Nabben","submitted_at":"2012-06-07T14:30:03Z","abstract_excerpt":"We consider deflation and augmentation techniques for accelerating the convergence of Krylov subspace methods for the solution of nonsingular linear algebraic systems. Despite some formal similarity, the two techniques are conceptually different from preconditioning. Deflation (in the sense the term is used here) \"removes\" certain parts from the operator making it singular, while augmentation adds a subspace to the Krylov subspace (often the one that is generated by the singular operator); in contrast, preconditioning changes the spectrum of the operator without making it singular. Deflation a"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1206.1506","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-06-07T14:30:03Z","cross_cats_sorted":[],"title_canon_sha256":"f3bc1f5648cb3472ba34f37bbb96426110e32999b05a2d251da0f81baaebada8","abstract_canon_sha256":"e43bfe7f790ceae6109758fbed7f8331f1b080934124a94499ce8247db7e91b1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:59.948496Z","signature_b64":"lrNUJUsORkcVfIKkPHWCQCAkNQsa+FC7/g8fnCIIqNe/CIX4K6+AH+39ps8aUsNODCs4le8st8F/qY6Ygt08BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4fc7ac439d20d1106ae63dcd5374dcbd51fc5bd1f7b8c199ff3fb485413497af","last_reissued_at":"2026-05-18T01:29:59.947998Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:59.947998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A framework for deflated and augmented Krylov subspace methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Andr\\'e Gaul, J\\\"org Liesen, Martin H. Gutknecht, Reinhard Nabben","submitted_at":"2012-06-07T14:30:03Z","abstract_excerpt":"We consider deflation and augmentation techniques for accelerating the convergence of Krylov subspace methods for the solution of nonsingular linear algebraic systems. Despite some formal similarity, the two techniques are conceptually different from preconditioning. Deflation (in the sense the term is used here) \"removes\" certain parts from the operator making it singular, while augmentation adds a subspace to the Krylov subspace (often the one that is generated by the singular operator); in contrast, preconditioning changes the spectrum of the operator without making it singular. Deflation a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.1506","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1206.1506","created_at":"2026-05-18T01:29:59.948071+00:00"},{"alias_kind":"arxiv_version","alias_value":"1206.1506v2","created_at":"2026-05-18T01:29:59.948071+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.1506","created_at":"2026-05-18T01:29:59.948071+00:00"},{"alias_kind":"pith_short_12","alias_value":"J7D2YQ45EDIR","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_16","alias_value":"J7D2YQ45EDIRA2XG","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_8","alias_value":"J7D2YQ45","created_at":"2026-05-18T12:27:11.947152+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/J7D2YQ45EDIRA2XGHXGVG5G4XV","json":"https://pith.science/pith/J7D2YQ45EDIRA2XGHXGVG5G4XV.json","graph_json":"https://pith.science/api/pith-number/J7D2YQ45EDIRA2XGHXGVG5G4XV/graph.json","events_json":"https://pith.science/api/pith-number/J7D2YQ45EDIRA2XGHXGVG5G4XV/events.json","paper":"https://pith.science/paper/J7D2YQ45"},"agent_actions":{"view_html":"https://pith.science/pith/J7D2YQ45EDIRA2XGHXGVG5G4XV","download_json":"https://pith.science/pith/J7D2YQ45EDIRA2XGHXGVG5G4XV.json","view_paper":"https://pith.science/paper/J7D2YQ45","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1206.1506&json=true","fetch_graph":"https://pith.science/api/pith-number/J7D2YQ45EDIRA2XGHXGVG5G4XV/graph.json","fetch_events":"https://pith.science/api/pith-number/J7D2YQ45EDIRA2XGHXGVG5G4XV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J7D2YQ45EDIRA2XGHXGVG5G4XV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J7D2YQ45EDIRA2XGHXGVG5G4XV/action/storage_attestation","attest_author":"https://pith.science/pith/J7D2YQ45EDIRA2XGHXGVG5G4XV/action/author_attestation","sign_citation":"https://pith.science/pith/J7D2YQ45EDIRA2XGHXGVG5G4XV/action/citation_signature","submit_replication":"https://pith.science/pith/J7D2YQ45EDIRA2XGHXGVG5G4XV/action/replication_record"}},"created_at":"2026-05-18T01:29:59.948071+00:00","updated_at":"2026-05-18T01:29:59.948071+00:00"}