{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:FGOOSC7MHWUWTJPMGXNCOF3VPW","short_pith_number":"pith:FGOOSC7M","schema_version":"1.0","canonical_sha256":"299ce90bec3da969a5ec35da2717757d94b1dea4fb96ec8071ccd4f75ec0059d","source":{"kind":"arxiv","id":"1309.3926","version":3},"attestation_state":"computed","paper":{"title":"A positivity preserving inexact Noda iteration for computing the smallest eigenpair of a large irreducible M-matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Ching-Sung Liu, Wen-Wei Lin, Zhongxiao Jia","submitted_at":"2013-09-16T12:22:09Z","abstract_excerpt":"In this paper, based on the Noda iteration, we present inexact Noda iterations (INI), to find the smallest eigenvalue and the associated positive eigenvector of a large irreducible nonsingular M-matrix. The positivity of approximations is critical in applications, and if the approximations lose the positivity then they will be physically meaningless. We propose two different inner tolerance strategies for solving the inner linear systems involved, and prove that the resulting INI algorithms are globally linear and superlinear with the convergence order $\\frac{1+\\sqrt{5}}{2}$, respectively. The"},"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":"1309.3926","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-09-16T12:22:09Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"6a91eb5376ccab08840b3d7a5563ecf908cd21b88315df36f3a995f0ed873684","abstract_canon_sha256":"452e4293e73b9c11d2e087282d13f09aa5712e421c08dc4353ea88bc4428f21f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T14:09:11.104680Z","signature_b64":"1Vn19yeii1pJ43hEs5C8GpwJSFWGrXXHfWEvH5IzhHDSFoeiRiKWFlBIoyl2T6foFjyDOfDJsKY9YiqyTO8ZCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"299ce90bec3da969a5ec35da2717757d94b1dea4fb96ec8071ccd4f75ec0059d","last_reissued_at":"2026-06-04T14:09:11.104150Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T14:09:11.104150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A positivity preserving inexact Noda iteration for computing the smallest eigenpair of a large irreducible M-matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Ching-Sung Liu, Wen-Wei Lin, Zhongxiao Jia","submitted_at":"2013-09-16T12:22:09Z","abstract_excerpt":"In this paper, based on the Noda iteration, we present inexact Noda iterations (INI), to find the smallest eigenvalue and the associated positive eigenvector of a large irreducible nonsingular M-matrix. The positivity of approximations is critical in applications, and if the approximations lose the positivity then they will be physically meaningless. We propose two different inner tolerance strategies for solving the inner linear systems involved, and prove that the resulting INI algorithms are globally linear and superlinear with the convergence order $\\frac{1+\\sqrt{5}}{2}$, respectively. The"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.3926","kind":"arxiv","version":3},"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/1309.3926/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":"1309.3926","created_at":"2026-06-04T14:09:11.104210+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.3926v3","created_at":"2026-06-04T14:09:11.104210+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.3926","created_at":"2026-06-04T14:09:11.104210+00:00"},{"alias_kind":"pith_short_12","alias_value":"FGOOSC7MHWUW","created_at":"2026-06-04T14:09:11.104210+00:00"},{"alias_kind":"pith_short_16","alias_value":"FGOOSC7MHWUWTJPM","created_at":"2026-06-04T14:09:11.104210+00:00"},{"alias_kind":"pith_short_8","alias_value":"FGOOSC7M","created_at":"2026-06-04T14:09:11.104210+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/FGOOSC7MHWUWTJPMGXNCOF3VPW","json":"https://pith.science/pith/FGOOSC7MHWUWTJPMGXNCOF3VPW.json","graph_json":"https://pith.science/api/pith-number/FGOOSC7MHWUWTJPMGXNCOF3VPW/graph.json","events_json":"https://pith.science/api/pith-number/FGOOSC7MHWUWTJPMGXNCOF3VPW/events.json","paper":"https://pith.science/paper/FGOOSC7M"},"agent_actions":{"view_html":"https://pith.science/pith/FGOOSC7MHWUWTJPMGXNCOF3VPW","download_json":"https://pith.science/pith/FGOOSC7MHWUWTJPMGXNCOF3VPW.json","view_paper":"https://pith.science/paper/FGOOSC7M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.3926&json=true","fetch_graph":"https://pith.science/api/pith-number/FGOOSC7MHWUWTJPMGXNCOF3VPW/graph.json","fetch_events":"https://pith.science/api/pith-number/FGOOSC7MHWUWTJPMGXNCOF3VPW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FGOOSC7MHWUWTJPMGXNCOF3VPW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FGOOSC7MHWUWTJPMGXNCOF3VPW/action/storage_attestation","attest_author":"https://pith.science/pith/FGOOSC7MHWUWTJPMGXNCOF3VPW/action/author_attestation","sign_citation":"https://pith.science/pith/FGOOSC7MHWUWTJPMGXNCOF3VPW/action/citation_signature","submit_replication":"https://pith.science/pith/FGOOSC7MHWUWTJPMGXNCOF3VPW/action/replication_record"}},"created_at":"2026-06-04T14:09:11.104210+00:00","updated_at":"2026-06-04T14:09:11.104210+00:00"}