{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:5AO3AIPKQLGJR6KQTEQ274L3Z5","short_pith_number":"pith:5AO3AIPK","schema_version":"1.0","canonical_sha256":"e81db021ea82cc98f9509921aff17bcf6d1d7c9361c693b8e923c276ac054d48","source":{"kind":"arxiv","id":"1204.5463","version":1},"attestation_state":"computed","paper":{"title":"Deflation and Flexible SAP-Preconditioning of GMRES in Lattice QCD Simulation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-lat","authors_text":"Andrea Nobile, Andreas Frommer, Paul Zingler","submitted_at":"2012-04-24T19:25:26Z","abstract_excerpt":"The simulation of lattice QCD on massively parallel computers stimulated the development of scalable algorithms for the solution of sparse linear systems. We tackle the problem of the Wilson-Dirac operator inversion by combining a Schwarz alternating procedure (SAP) in multiplicative form with a flexible variant of the GMRES-DR algorithm. We show that restarted GMRES is not able to converge when the system is poorly conditioned. By adding deflation in the form of the FGMRES-DR algorithm, an important fraction of the information produced by the iterates is kept between successive restarts leadi"},"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":"1204.5463","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2012-04-24T19:25:26Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"d786667d12d7b4fee7330d5376b998d2b3d2e72bda0e1bb91147220036df61eb","abstract_canon_sha256":"393efd7a8ea83512a23e424737ce495d7b3f9da35e70035b12245f641f2abc5c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:13.222918Z","signature_b64":"PDShPNINz37incujLeHWz43pIAaFF6GMjKTOnIJBoKvKkIO6+mUmsFv/3yfvPTNXm/ZAnyr8NKydFXc5f10WDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e81db021ea82cc98f9509921aff17bcf6d1d7c9361c693b8e923c276ac054d48","last_reissued_at":"2026-05-18T03:57:13.222383Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:13.222383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Deflation and Flexible SAP-Preconditioning of GMRES in Lattice QCD Simulation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-lat","authors_text":"Andrea Nobile, Andreas Frommer, Paul Zingler","submitted_at":"2012-04-24T19:25:26Z","abstract_excerpt":"The simulation of lattice QCD on massively parallel computers stimulated the development of scalable algorithms for the solution of sparse linear systems. We tackle the problem of the Wilson-Dirac operator inversion by combining a Schwarz alternating procedure (SAP) in multiplicative form with a flexible variant of the GMRES-DR algorithm. We show that restarted GMRES is not able to converge when the system is poorly conditioned. By adding deflation in the form of the FGMRES-DR algorithm, an important fraction of the information produced by the iterates is kept between successive restarts leadi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5463","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":""},"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":"1204.5463","created_at":"2026-05-18T03:57:13.222464+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.5463v1","created_at":"2026-05-18T03:57:13.222464+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.5463","created_at":"2026-05-18T03:57:13.222464+00:00"},{"alias_kind":"pith_short_12","alias_value":"5AO3AIPKQLGJ","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_16","alias_value":"5AO3AIPKQLGJR6KQ","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_8","alias_value":"5AO3AIPK","created_at":"2026-05-18T12:26:53.410803+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/5AO3AIPKQLGJR6KQTEQ274L3Z5","json":"https://pith.science/pith/5AO3AIPKQLGJR6KQTEQ274L3Z5.json","graph_json":"https://pith.science/api/pith-number/5AO3AIPKQLGJR6KQTEQ274L3Z5/graph.json","events_json":"https://pith.science/api/pith-number/5AO3AIPKQLGJR6KQTEQ274L3Z5/events.json","paper":"https://pith.science/paper/5AO3AIPK"},"agent_actions":{"view_html":"https://pith.science/pith/5AO3AIPKQLGJR6KQTEQ274L3Z5","download_json":"https://pith.science/pith/5AO3AIPKQLGJR6KQTEQ274L3Z5.json","view_paper":"https://pith.science/paper/5AO3AIPK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.5463&json=true","fetch_graph":"https://pith.science/api/pith-number/5AO3AIPKQLGJR6KQTEQ274L3Z5/graph.json","fetch_events":"https://pith.science/api/pith-number/5AO3AIPKQLGJR6KQTEQ274L3Z5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5AO3AIPKQLGJR6KQTEQ274L3Z5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5AO3AIPKQLGJR6KQTEQ274L3Z5/action/storage_attestation","attest_author":"https://pith.science/pith/5AO3AIPKQLGJR6KQTEQ274L3Z5/action/author_attestation","sign_citation":"https://pith.science/pith/5AO3AIPKQLGJR6KQTEQ274L3Z5/action/citation_signature","submit_replication":"https://pith.science/pith/5AO3AIPKQLGJR6KQTEQ274L3Z5/action/replication_record"}},"created_at":"2026-05-18T03:57:13.222464+00:00","updated_at":"2026-05-18T03:57:13.222464+00:00"}