{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:TCUJ5IKWPRQHPUHW4MUTJLJKJP","short_pith_number":"pith:TCUJ5IKW","schema_version":"1.0","canonical_sha256":"98a89ea1567c6077d0f6e32934ad2a4bf2605517e187c108c4d9d4236c696111","source":{"kind":"arxiv","id":"1901.01188","version":2},"attestation_state":"computed","paper":{"title":"A rational approximation method for the nonlinear eigenvalue problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Agnieszka Mi\\k{e}dlar, Mohamed El-Guide, Yousef Saad","submitted_at":"2019-01-04T16:03:04Z","abstract_excerpt":"This paper presents a method for computing eigenvalues and eigenvectors for some types of nonlinear eigenvalue problems. The main idea is to approximate the functions involved in the eigenvalue problem by rational functions and then apply a form of linearization. Eigenpairs of the expanded form of this linearization are not extracted directly. Instead, its structure is exploited to develop a scheme that allows to extract all eigenvalues in a certain region of the complex plane by solving an eigenvalue problem of much smaller dimension. Because of its simple implementation and the ability to wo"},"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":"1901.01188","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-01-04T16:03:04Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"2791fb39ff5d2d8ec365368e3de8f49bf13bb68c4bbf7f1a2cb0dfdc94ab7eba","abstract_canon_sha256":"24c3459f416596fab4caaabae22a66935fc5f56188600f96acecd12b257cdf54"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:08:58.653553Z","signature_b64":"6PvTzC9vUBubgpdORtEn/YNUKdlKiT+wmnQPcUzk/EEKe/aFIg7Sl2+QdOxAHZ0FX/LVVTu8qyoTTtKKwspADw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"98a89ea1567c6077d0f6e32934ad2a4bf2605517e187c108c4d9d4236c696111","last_reissued_at":"2026-07-05T01:08:58.653088Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:08:58.653088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A rational approximation method for the nonlinear eigenvalue problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Agnieszka Mi\\k{e}dlar, Mohamed El-Guide, Yousef Saad","submitted_at":"2019-01-04T16:03:04Z","abstract_excerpt":"This paper presents a method for computing eigenvalues and eigenvectors for some types of nonlinear eigenvalue problems. The main idea is to approximate the functions involved in the eigenvalue problem by rational functions and then apply a form of linearization. Eigenpairs of the expanded form of this linearization are not extracted directly. Instead, its structure is exploited to develop a scheme that allows to extract all eigenvalues in a certain region of the complex plane by solving an eigenvalue problem of much smaller dimension. Because of its simple implementation and the ability to wo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.01188","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/1901.01188/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":"1901.01188","created_at":"2026-07-05T01:08:58.653140+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.01188v2","created_at":"2026-07-05T01:08:58.653140+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.01188","created_at":"2026-07-05T01:08:58.653140+00:00"},{"alias_kind":"pith_short_12","alias_value":"TCUJ5IKWPRQH","created_at":"2026-07-05T01:08:58.653140+00:00"},{"alias_kind":"pith_short_16","alias_value":"TCUJ5IKWPRQHPUHW","created_at":"2026-07-05T01:08:58.653140+00:00"},{"alias_kind":"pith_short_8","alias_value":"TCUJ5IKW","created_at":"2026-07-05T01:08:58.653140+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.13357","citing_title":"Linear convergence of iterative contour integral-based eigensolvers for nonlinear eigenvalue problems","ref_index":27,"is_internal_anchor":false},{"citing_arxiv_id":"1907.10972","citing_title":"Local Linearizations of Rational Matrices with Application to Rational Approximations of Nonlinear Eigenvalue Problems","ref_index":29,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TCUJ5IKWPRQHPUHW4MUTJLJKJP","json":"https://pith.science/pith/TCUJ5IKWPRQHPUHW4MUTJLJKJP.json","graph_json":"https://pith.science/api/pith-number/TCUJ5IKWPRQHPUHW4MUTJLJKJP/graph.json","events_json":"https://pith.science/api/pith-number/TCUJ5IKWPRQHPUHW4MUTJLJKJP/events.json","paper":"https://pith.science/paper/TCUJ5IKW"},"agent_actions":{"view_html":"https://pith.science/pith/TCUJ5IKWPRQHPUHW4MUTJLJKJP","download_json":"https://pith.science/pith/TCUJ5IKWPRQHPUHW4MUTJLJKJP.json","view_paper":"https://pith.science/paper/TCUJ5IKW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.01188&json=true","fetch_graph":"https://pith.science/api/pith-number/TCUJ5IKWPRQHPUHW4MUTJLJKJP/graph.json","fetch_events":"https://pith.science/api/pith-number/TCUJ5IKWPRQHPUHW4MUTJLJKJP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TCUJ5IKWPRQHPUHW4MUTJLJKJP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TCUJ5IKWPRQHPUHW4MUTJLJKJP/action/storage_attestation","attest_author":"https://pith.science/pith/TCUJ5IKWPRQHPUHW4MUTJLJKJP/action/author_attestation","sign_citation":"https://pith.science/pith/TCUJ5IKWPRQHPUHW4MUTJLJKJP/action/citation_signature","submit_replication":"https://pith.science/pith/TCUJ5IKWPRQHPUHW4MUTJLJKJP/action/replication_record"}},"created_at":"2026-07-05T01:08:58.653140+00:00","updated_at":"2026-07-05T01:08:58.653140+00:00"}