{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:6OUTJNUCMVLN5RREROJVGQ4ZCZ","short_pith_number":"pith:6OUTJNUC","schema_version":"1.0","canonical_sha256":"f3a934b6826556dec6248b93534399167d4f0ea97aaab6d5ae8c1cbad43fa9d8","source":{"kind":"arxiv","id":"1312.5677","version":2},"attestation_state":"computed","paper":{"title":"On the accuracy and stability of algorithms most commonly used in the evaluation of Chebyshev polynomials of the first kind","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Agata Smoktunowicz, Alicja Smoktunowicz, Ewa Pawelec","submitted_at":"2013-12-19T18:11:01Z","abstract_excerpt":"This paper provides error analyses of the algorithms most commonly used for the evaluation of the Chebyshev polynomial of the first kind $T_N(x)$. Some of these algorithms are shown to be backward stable. This means that the computed value of $T_N(x)$ in floating point arithmetic by these algorithms can be interpreted as a slightly perturbed value of polynomial $T_N$, for slightly perturbed value of $x$."},"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":"1312.5677","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-12-19T18:11:01Z","cross_cats_sorted":[],"title_canon_sha256":"d3e095a394d294436073c38419514f32d1accb556b42adf3044f3b69a8131614","abstract_canon_sha256":"a21c147233c5c79358f19d8891ea50991e52283f13ee63a02050581a02f7df2d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:07.983063Z","signature_b64":"8xGdJGyE2VC7agvQnfqphNAQswL6ghjs/DqC6/6qnVnb4/4n/Gl9+z7hGF9D1iPbWohPcjEeq5esdnsoM46ICA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3a934b6826556dec6248b93534399167d4f0ea97aaab6d5ae8c1cbad43fa9d8","last_reissued_at":"2026-05-18T03:04:07.982423Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:07.982423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the accuracy and stability of algorithms most commonly used in the evaluation of Chebyshev polynomials of the first kind","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Agata Smoktunowicz, Alicja Smoktunowicz, Ewa Pawelec","submitted_at":"2013-12-19T18:11:01Z","abstract_excerpt":"This paper provides error analyses of the algorithms most commonly used for the evaluation of the Chebyshev polynomial of the first kind $T_N(x)$. Some of these algorithms are shown to be backward stable. This means that the computed value of $T_N(x)$ in floating point arithmetic by these algorithms can be interpreted as a slightly perturbed value of polynomial $T_N$, for slightly perturbed value of $x$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.5677","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":""},"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":"1312.5677","created_at":"2026-05-18T03:04:07.982511+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.5677v2","created_at":"2026-05-18T03:04:07.982511+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.5677","created_at":"2026-05-18T03:04:07.982511+00:00"},{"alias_kind":"pith_short_12","alias_value":"6OUTJNUCMVLN","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_16","alias_value":"6OUTJNUCMVLN5RRE","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_8","alias_value":"6OUTJNUC","created_at":"2026-05-18T12:27:36.564083+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/6OUTJNUCMVLN5RREROJVGQ4ZCZ","json":"https://pith.science/pith/6OUTJNUCMVLN5RREROJVGQ4ZCZ.json","graph_json":"https://pith.science/api/pith-number/6OUTJNUCMVLN5RREROJVGQ4ZCZ/graph.json","events_json":"https://pith.science/api/pith-number/6OUTJNUCMVLN5RREROJVGQ4ZCZ/events.json","paper":"https://pith.science/paper/6OUTJNUC"},"agent_actions":{"view_html":"https://pith.science/pith/6OUTJNUCMVLN5RREROJVGQ4ZCZ","download_json":"https://pith.science/pith/6OUTJNUCMVLN5RREROJVGQ4ZCZ.json","view_paper":"https://pith.science/paper/6OUTJNUC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.5677&json=true","fetch_graph":"https://pith.science/api/pith-number/6OUTJNUCMVLN5RREROJVGQ4ZCZ/graph.json","fetch_events":"https://pith.science/api/pith-number/6OUTJNUCMVLN5RREROJVGQ4ZCZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6OUTJNUCMVLN5RREROJVGQ4ZCZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6OUTJNUCMVLN5RREROJVGQ4ZCZ/action/storage_attestation","attest_author":"https://pith.science/pith/6OUTJNUCMVLN5RREROJVGQ4ZCZ/action/author_attestation","sign_citation":"https://pith.science/pith/6OUTJNUCMVLN5RREROJVGQ4ZCZ/action/citation_signature","submit_replication":"https://pith.science/pith/6OUTJNUCMVLN5RREROJVGQ4ZCZ/action/replication_record"}},"created_at":"2026-05-18T03:04:07.982511+00:00","updated_at":"2026-05-18T03:04:07.982511+00:00"}