{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:G2NCTHVH44DU5ZOQWEMXCGYPYA","short_pith_number":"pith:G2NCTHVH","schema_version":"1.0","canonical_sha256":"369a299ea7e7074ee5d0b119711b0fc01a2eee47d4389c4ddac24659b377177d","source":{"kind":"arxiv","id":"2406.07044","version":1},"attestation_state":"computed","paper":{"title":"On inertial Levenberg-Marquardt type methods for solving nonlinear ill-posed operator equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Antonio Leit\\~ao, Dirk A. Lorenz, Joel C. Rabelo, Maximilian Winkler","submitted_at":"2024-06-11T08:11:22Z","abstract_excerpt":"In these notes we propose and analyze an inertial type method for obtaining stable approximate solutions to nonlinear ill-posed operator equations. The method is based on the Levenberg-Marquardt (LM) iteration. The main obtained results are: monotonicity and convergence for exact data, stability and semi-convergence for noisy data. Regarding numerical experiments we consider: i) a parameter identification problem in elliptic PDEs, ii) a parameter identification problem in machine learning; the computational efficiency of the proposed method is compared with canonical implementations of the LM "},"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":"2406.07044","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-06-11T08:11:22Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"b4cd3a913963ccd42587adbce43db89020f3d40097ff2ca080af9f06acc32521","abstract_canon_sha256":"4196dbf80fca1ea29957266d593611e787f1270f1a86cc886257a4fb26532932"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:30:17.478224Z","signature_b64":"QE0FzaDzcYwIMRIzb9/nF+GA7u8dn97UjwmymZgZ7DW7soRJa0uWdfe6ruQpggExVGGc9J5LtIODPqs3Hku1BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"369a299ea7e7074ee5d0b119711b0fc01a2eee47d4389c4ddac24659b377177d","last_reissued_at":"2026-07-05T08:30:17.477725Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:30:17.477725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On inertial Levenberg-Marquardt type methods for solving nonlinear ill-posed operator equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Antonio Leit\\~ao, Dirk A. Lorenz, Joel C. Rabelo, Maximilian Winkler","submitted_at":"2024-06-11T08:11:22Z","abstract_excerpt":"In these notes we propose and analyze an inertial type method for obtaining stable approximate solutions to nonlinear ill-posed operator equations. The method is based on the Levenberg-Marquardt (LM) iteration. The main obtained results are: monotonicity and convergence for exact data, stability and semi-convergence for noisy data. Regarding numerical experiments we consider: i) a parameter identification problem in elliptic PDEs, ii) a parameter identification problem in machine learning; the computational efficiency of the proposed method is compared with canonical implementations of the LM "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.07044","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2406.07044/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":"2406.07044","created_at":"2026-07-05T08:30:17.477779+00:00"},{"alias_kind":"arxiv_version","alias_value":"2406.07044v1","created_at":"2026-07-05T08:30:17.477779+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.07044","created_at":"2026-07-05T08:30:17.477779+00:00"},{"alias_kind":"pith_short_12","alias_value":"G2NCTHVH44DU","created_at":"2026-07-05T08:30:17.477779+00:00"},{"alias_kind":"pith_short_16","alias_value":"G2NCTHVH44DU5ZOQ","created_at":"2026-07-05T08:30:17.477779+00:00"},{"alias_kind":"pith_short_8","alias_value":"G2NCTHVH","created_at":"2026-07-05T08:30:17.477779+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/G2NCTHVH44DU5ZOQWEMXCGYPYA","json":"https://pith.science/pith/G2NCTHVH44DU5ZOQWEMXCGYPYA.json","graph_json":"https://pith.science/api/pith-number/G2NCTHVH44DU5ZOQWEMXCGYPYA/graph.json","events_json":"https://pith.science/api/pith-number/G2NCTHVH44DU5ZOQWEMXCGYPYA/events.json","paper":"https://pith.science/paper/G2NCTHVH"},"agent_actions":{"view_html":"https://pith.science/pith/G2NCTHVH44DU5ZOQWEMXCGYPYA","download_json":"https://pith.science/pith/G2NCTHVH44DU5ZOQWEMXCGYPYA.json","view_paper":"https://pith.science/paper/G2NCTHVH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2406.07044&json=true","fetch_graph":"https://pith.science/api/pith-number/G2NCTHVH44DU5ZOQWEMXCGYPYA/graph.json","fetch_events":"https://pith.science/api/pith-number/G2NCTHVH44DU5ZOQWEMXCGYPYA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G2NCTHVH44DU5ZOQWEMXCGYPYA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G2NCTHVH44DU5ZOQWEMXCGYPYA/action/storage_attestation","attest_author":"https://pith.science/pith/G2NCTHVH44DU5ZOQWEMXCGYPYA/action/author_attestation","sign_citation":"https://pith.science/pith/G2NCTHVH44DU5ZOQWEMXCGYPYA/action/citation_signature","submit_replication":"https://pith.science/pith/G2NCTHVH44DU5ZOQWEMXCGYPYA/action/replication_record"}},"created_at":"2026-07-05T08:30:17.477779+00:00","updated_at":"2026-07-05T08:30:17.477779+00:00"}