{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:KHKLRD4JK2F5TQKE5TBVYTCLXB","short_pith_number":"pith:KHKLRD4J","schema_version":"1.0","canonical_sha256":"51d4b88f89568bd9c144ecc35c4c4bb865512bdc00015b07faccbd20e9bb9fb4","source":{"kind":"arxiv","id":"1604.04569","version":1},"attestation_state":"computed","paper":{"title":"Kantorovich's theorem on Newton's method for solving strongly regular generalized equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.NA","authors_text":"G. N. Silva, O. P. Ferreira","submitted_at":"2016-04-15T16:55:16Z","abstract_excerpt":"In this paper we consider the Newton's method for solving the generalized equation of the form $ f(x) +F(x) \\ni 0, $ where $f:{\\Omega}\\to Y$ is a continuously differentiable mapping, $X$ and $Y$ are Banach spaces, $\\Omega\\subseteq X$ an open set and $F:X \\rightrightarrows Y$ be a set-valued mapping with nonempty closed graph. We show that, under strong regularity of the generalized equation, concept introduced by S.M.Robinson in [27], and starting point satisfying the Kantorovich's assumptions, the Newton's method is quadratically convergent to a solution, which is unique in a suitable neighbo"},"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":"1604.04569","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-04-15T16:55:16Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"431b24bd1aca797b2f3bf01dbb16a8313ac713d908b4c893a2aaba3f745a3713","abstract_canon_sha256":"71e87d341845488d8a83f6999288bfd808c1b1dfdf07158110897638dd7260e1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:01.841668Z","signature_b64":"E1dKLm6XvcPNwZDYURkDvX549QchcwpMDec+w5f1F3ATrX4LMHxXKIoSEKedkED2fgWbHFjOOIGGFRCZFcgQBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51d4b88f89568bd9c144ecc35c4c4bb865512bdc00015b07faccbd20e9bb9fb4","last_reissued_at":"2026-05-18T01:17:01.840843Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:01.840843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Kantorovich's theorem on Newton's method for solving strongly regular generalized equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.NA","authors_text":"G. N. Silva, O. P. Ferreira","submitted_at":"2016-04-15T16:55:16Z","abstract_excerpt":"In this paper we consider the Newton's method for solving the generalized equation of the form $ f(x) +F(x) \\ni 0, $ where $f:{\\Omega}\\to Y$ is a continuously differentiable mapping, $X$ and $Y$ are Banach spaces, $\\Omega\\subseteq X$ an open set and $F:X \\rightrightarrows Y$ be a set-valued mapping with nonempty closed graph. We show that, under strong regularity of the generalized equation, concept introduced by S.M.Robinson in [27], and starting point satisfying the Kantorovich's assumptions, the Newton's method is quadratically convergent to a solution, which is unique in a suitable neighbo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04569","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":"1604.04569","created_at":"2026-05-18T01:17:01.840983+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.04569v1","created_at":"2026-05-18T01:17:01.840983+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.04569","created_at":"2026-05-18T01:17:01.840983+00:00"},{"alias_kind":"pith_short_12","alias_value":"KHKLRD4JK2F5","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_16","alias_value":"KHKLRD4JK2F5TQKE","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_8","alias_value":"KHKLRD4J","created_at":"2026-05-18T12:30:25.849896+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/KHKLRD4JK2F5TQKE5TBVYTCLXB","json":"https://pith.science/pith/KHKLRD4JK2F5TQKE5TBVYTCLXB.json","graph_json":"https://pith.science/api/pith-number/KHKLRD4JK2F5TQKE5TBVYTCLXB/graph.json","events_json":"https://pith.science/api/pith-number/KHKLRD4JK2F5TQKE5TBVYTCLXB/events.json","paper":"https://pith.science/paper/KHKLRD4J"},"agent_actions":{"view_html":"https://pith.science/pith/KHKLRD4JK2F5TQKE5TBVYTCLXB","download_json":"https://pith.science/pith/KHKLRD4JK2F5TQKE5TBVYTCLXB.json","view_paper":"https://pith.science/paper/KHKLRD4J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.04569&json=true","fetch_graph":"https://pith.science/api/pith-number/KHKLRD4JK2F5TQKE5TBVYTCLXB/graph.json","fetch_events":"https://pith.science/api/pith-number/KHKLRD4JK2F5TQKE5TBVYTCLXB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KHKLRD4JK2F5TQKE5TBVYTCLXB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KHKLRD4JK2F5TQKE5TBVYTCLXB/action/storage_attestation","attest_author":"https://pith.science/pith/KHKLRD4JK2F5TQKE5TBVYTCLXB/action/author_attestation","sign_citation":"https://pith.science/pith/KHKLRD4JK2F5TQKE5TBVYTCLXB/action/citation_signature","submit_replication":"https://pith.science/pith/KHKLRD4JK2F5TQKE5TBVYTCLXB/action/replication_record"}},"created_at":"2026-05-18T01:17:01.840983+00:00","updated_at":"2026-05-18T01:17:01.840983+00:00"}