{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:E65OG57NKTEXEOPKBFIUHRAFS5","short_pith_number":"pith:E65OG57N","schema_version":"1.0","canonical_sha256":"27bae377ed54c97239ea095143c405974c6e4f25f37ef550c90d6e589614df87","source":{"kind":"arxiv","id":"2204.07918","version":2},"attestation_state":"computed","paper":{"title":"Convergence analysis of two-grid methods for nonsymmetric positive definite systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Xuefeng Xu","submitted_at":"2022-04-17T04:22:02Z","abstract_excerpt":"The convergence theory of multigrid methods for symmetric positive definite systems is well established. For nonsymmetric systems, however, the corresponding theory remains far from mature. Two-grid analysis is fundamental to the design and analysis of multigrid methods. This paper presents a convergence analysis of two-grid methods for nonsymmetric positive definite systems. When the coarse-grid system is solved exactly, we derive a succinct identity for the two-grid convergence factor measured in a smoother-induced norm. More generally, under mild assumptions, we develop a convergence theory"},"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":"2204.07918","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-04-17T04:22:02Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"da00dcd3451181be079085719592676b0ab8aaf1aad0f7029b829cf20904a1a9","abstract_canon_sha256":"b6e4b9eac8883e656c93d4d5cd52107ce5eded6ce10a2cb21709657d4ace984c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T01:17:18.019820Z","signature_b64":"RMgBLgoFff6qJJMwD7m4m0YSHStZDSdpF++4HmKJR7YOZQpOEduyqgoM/BvfzyaKmUO6avpKTjWaLcm8DVOGCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"27bae377ed54c97239ea095143c405974c6e4f25f37ef550c90d6e589614df87","last_reissued_at":"2026-06-30T01:17:18.019028Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T01:17:18.019028Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convergence analysis of two-grid methods for nonsymmetric positive definite systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Xuefeng Xu","submitted_at":"2022-04-17T04:22:02Z","abstract_excerpt":"The convergence theory of multigrid methods for symmetric positive definite systems is well established. For nonsymmetric systems, however, the corresponding theory remains far from mature. Two-grid analysis is fundamental to the design and analysis of multigrid methods. This paper presents a convergence analysis of two-grid methods for nonsymmetric positive definite systems. When the coarse-grid system is solved exactly, we derive a succinct identity for the two-grid convergence factor measured in a smoother-induced norm. More generally, under mild assumptions, we develop a convergence theory"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.07918","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2204.07918/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2204.07918","created_at":"2026-06-30T01:17:18.019113+00:00"},{"alias_kind":"arxiv_version","alias_value":"2204.07918v2","created_at":"2026-06-30T01:17:18.019113+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.07918","created_at":"2026-06-30T01:17:18.019113+00:00"},{"alias_kind":"pith_short_12","alias_value":"E65OG57NKTEX","created_at":"2026-06-30T01:17:18.019113+00:00"},{"alias_kind":"pith_short_16","alias_value":"E65OG57NKTEXEOPK","created_at":"2026-06-30T01:17:18.019113+00:00"},{"alias_kind":"pith_short_8","alias_value":"E65OG57N","created_at":"2026-06-30T01:17:18.019113+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2604.21815","citing_title":"Norm-based convergence bounds for nonsymmetric algebraic V-cycle multigrid methods","ref_index":37,"is_internal_anchor":true},{"citing_arxiv_id":"2604.21648","citing_title":"Optimal transfer operators for nonsymmetric two-grid methods","ref_index":39,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/E65OG57NKTEXEOPKBFIUHRAFS5","json":"https://pith.science/pith/E65OG57NKTEXEOPKBFIUHRAFS5.json","graph_json":"https://pith.science/api/pith-number/E65OG57NKTEXEOPKBFIUHRAFS5/graph.json","events_json":"https://pith.science/api/pith-number/E65OG57NKTEXEOPKBFIUHRAFS5/events.json","paper":"https://pith.science/paper/E65OG57N"},"agent_actions":{"view_html":"https://pith.science/pith/E65OG57NKTEXEOPKBFIUHRAFS5","download_json":"https://pith.science/pith/E65OG57NKTEXEOPKBFIUHRAFS5.json","view_paper":"https://pith.science/paper/E65OG57N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2204.07918&json=true","fetch_graph":"https://pith.science/api/pith-number/E65OG57NKTEXEOPKBFIUHRAFS5/graph.json","fetch_events":"https://pith.science/api/pith-number/E65OG57NKTEXEOPKBFIUHRAFS5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E65OG57NKTEXEOPKBFIUHRAFS5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E65OG57NKTEXEOPKBFIUHRAFS5/action/storage_attestation","attest_author":"https://pith.science/pith/E65OG57NKTEXEOPKBFIUHRAFS5/action/author_attestation","sign_citation":"https://pith.science/pith/E65OG57NKTEXEOPKBFIUHRAFS5/action/citation_signature","submit_replication":"https://pith.science/pith/E65OG57NKTEXEOPKBFIUHRAFS5/action/replication_record"}},"created_at":"2026-06-30T01:17:18.019113+00:00","updated_at":"2026-06-30T01:17:18.019113+00:00"}