{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:JG5TUD2J4Q4AO7AEG5237UKSTP","short_pith_number":"pith:JG5TUD2J","schema_version":"1.0","canonical_sha256":"49bb3a0f49e438077c043775bfd1529bd791d751d7f6a0311ee91ce7097c420e","source":{"kind":"arxiv","id":"1705.00729","version":3},"attestation_state":"computed","paper":{"title":"New Combinations of Polynomial Root-Finding Iterations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Victor Y. Pan","submitted_at":"2017-05-01T22:29:14Z","abstract_excerpt":"Some near-optimal polynomial root-finders of 2024-25, based on subdivision iterations, approximate all complex roots of a polynomial or all roots in a fixed Region of Interest in the complex plane. The iterations can be applied to a black box polynomial, represented by an oracle (black box subroutine) for its evaluation rather than in monomial basis - by coefficients. We propose further empirical acceleration, for which we combine these iterations with Ehrlich's (aka Aberth's), Newton's, or Schroeder's. Our combinations of Ehrlich/Newton/Schroeder's and subdivision iterations can be applied to"},"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":"1705.00729","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-05-01T22:29:14Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"48dce0e57d01d88859800245a55a9a9b0f314ce9c6160b47aa36348071df72ac","abstract_canon_sha256":"ae4410d6903d40e60af131e9bf1fa6aba762501fce655783b278f7be4442e038"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-29T01:04:49.226332Z","signature_b64":"ExJTyvPstnN2nJ9Zhyss7xtmfEysV8dahqGFP3AmytQ10v2X4eWHXlbIxYvliHR/sJL3H7m0KbPF/kf2tUmhBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"49bb3a0f49e438077c043775bfd1529bd791d751d7f6a0311ee91ce7097c420e","last_reissued_at":"2026-05-29T01:04:49.225683Z","signature_status":"signed_v1","first_computed_at":"2026-05-29T01:04:49.225683Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"New Combinations of Polynomial Root-Finding Iterations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Victor Y. Pan","submitted_at":"2017-05-01T22:29:14Z","abstract_excerpt":"Some near-optimal polynomial root-finders of 2024-25, based on subdivision iterations, approximate all complex roots of a polynomial or all roots in a fixed Region of Interest in the complex plane. The iterations can be applied to a black box polynomial, represented by an oracle (black box subroutine) for its evaluation rather than in monomial basis - by coefficients. We propose further empirical acceleration, for which we combine these iterations with Ehrlich's (aka Aberth's), Newton's, or Schroeder's. Our combinations of Ehrlich/Newton/Schroeder's and subdivision iterations can be applied to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00729","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/1705.00729/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":"1705.00729","created_at":"2026-05-29T01:04:49.225773+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.00729v3","created_at":"2026-05-29T01:04:49.225773+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.00729","created_at":"2026-05-29T01:04:49.225773+00:00"},{"alias_kind":"pith_short_12","alias_value":"JG5TUD2J4Q4A","created_at":"2026-05-29T01:04:49.225773+00:00"},{"alias_kind":"pith_short_16","alias_value":"JG5TUD2J4Q4AO7AE","created_at":"2026-05-29T01:04:49.225773+00:00"},{"alias_kind":"pith_short_8","alias_value":"JG5TUD2J","created_at":"2026-05-29T01:04:49.225773+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/JG5TUD2J4Q4AO7AEG5237UKSTP","json":"https://pith.science/pith/JG5TUD2J4Q4AO7AEG5237UKSTP.json","graph_json":"https://pith.science/api/pith-number/JG5TUD2J4Q4AO7AEG5237UKSTP/graph.json","events_json":"https://pith.science/api/pith-number/JG5TUD2J4Q4AO7AEG5237UKSTP/events.json","paper":"https://pith.science/paper/JG5TUD2J"},"agent_actions":{"view_html":"https://pith.science/pith/JG5TUD2J4Q4AO7AEG5237UKSTP","download_json":"https://pith.science/pith/JG5TUD2J4Q4AO7AEG5237UKSTP.json","view_paper":"https://pith.science/paper/JG5TUD2J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.00729&json=true","fetch_graph":"https://pith.science/api/pith-number/JG5TUD2J4Q4AO7AEG5237UKSTP/graph.json","fetch_events":"https://pith.science/api/pith-number/JG5TUD2J4Q4AO7AEG5237UKSTP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JG5TUD2J4Q4AO7AEG5237UKSTP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JG5TUD2J4Q4AO7AEG5237UKSTP/action/storage_attestation","attest_author":"https://pith.science/pith/JG5TUD2J4Q4AO7AEG5237UKSTP/action/author_attestation","sign_citation":"https://pith.science/pith/JG5TUD2J4Q4AO7AEG5237UKSTP/action/citation_signature","submit_replication":"https://pith.science/pith/JG5TUD2J4Q4AO7AEG5237UKSTP/action/replication_record"}},"created_at":"2026-05-29T01:04:49.225773+00:00","updated_at":"2026-05-29T01:04:49.225773+00:00"}