{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:AB5QGUPXP6YVOU5FX4XFFE4Z2L","short_pith_number":"pith:AB5QGUPX","schema_version":"1.0","canonical_sha256":"007b0351f77fb15753a5bf2e529399d2d1e135527688e152bc4ebf97327470c7","source":{"kind":"arxiv","id":"1111.2283","version":2},"attestation_state":"computed","paper":{"title":"Roundoff errors in the problem of computing Cauchy principal value integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Iwona Wr\\'obel, Pawe{\\l} Keller","submitted_at":"2011-11-09T17:31:47Z","abstract_excerpt":"We investigate the possibility of fast, accurate and reliable computation of the Cauchy principal value integrals $\\mathrm{P}\\!\\int_{a}^{b} f(x)(x-\\tau)^{-1} dx$ $(a < \\tau < b)$ using standard adaptive quadratures. In order to properly control the error tolerance for the adaptive quadrature and to obtain a~reliable estimation of the approximation error, we research the possible influence of round-off errors on the computed result. As the numerical experiments confirm, the proposed method can successfully compete with other algorithms for computing such type integrals. Moreover, the presented "},"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":"1111.2283","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-11-09T17:31:47Z","cross_cats_sorted":[],"title_canon_sha256":"cf278f20c903e282b88f5254d8be5a35ab4b5fbf28b09299fa3cd5b4b1bc47b9","abstract_canon_sha256":"1eca9053bbd47157816840277595d11a0626531a4115ae27b5576e2cff7ad0b1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:40.114243Z","signature_b64":"aJEYEQ2WQzfSqTxxlajbVAmlDbKuyzLCh0LPcTl2+BLPDcxkIqI7bOmwtGfO411J1jVYxFoLzvQ/Rn/i5zwCCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"007b0351f77fb15753a5bf2e529399d2d1e135527688e152bc4ebf97327470c7","last_reissued_at":"2026-05-18T01:25:40.113508Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:40.113508Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Roundoff errors in the problem of computing Cauchy principal value integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Iwona Wr\\'obel, Pawe{\\l} Keller","submitted_at":"2011-11-09T17:31:47Z","abstract_excerpt":"We investigate the possibility of fast, accurate and reliable computation of the Cauchy principal value integrals $\\mathrm{P}\\!\\int_{a}^{b} f(x)(x-\\tau)^{-1} dx$ $(a < \\tau < b)$ using standard adaptive quadratures. In order to properly control the error tolerance for the adaptive quadrature and to obtain a~reliable estimation of the approximation error, we research the possible influence of round-off errors on the computed result. As the numerical experiments confirm, the proposed method can successfully compete with other algorithms for computing such type integrals. Moreover, the presented "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2283","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":"1111.2283","created_at":"2026-05-18T01:25:40.113642+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.2283v2","created_at":"2026-05-18T01:25:40.113642+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.2283","created_at":"2026-05-18T01:25:40.113642+00:00"},{"alias_kind":"pith_short_12","alias_value":"AB5QGUPXP6YV","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_16","alias_value":"AB5QGUPXP6YVOU5F","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_8","alias_value":"AB5QGUPX","created_at":"2026-05-18T12:26:24.575870+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/AB5QGUPXP6YVOU5FX4XFFE4Z2L","json":"https://pith.science/pith/AB5QGUPXP6YVOU5FX4XFFE4Z2L.json","graph_json":"https://pith.science/api/pith-number/AB5QGUPXP6YVOU5FX4XFFE4Z2L/graph.json","events_json":"https://pith.science/api/pith-number/AB5QGUPXP6YVOU5FX4XFFE4Z2L/events.json","paper":"https://pith.science/paper/AB5QGUPX"},"agent_actions":{"view_html":"https://pith.science/pith/AB5QGUPXP6YVOU5FX4XFFE4Z2L","download_json":"https://pith.science/pith/AB5QGUPXP6YVOU5FX4XFFE4Z2L.json","view_paper":"https://pith.science/paper/AB5QGUPX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.2283&json=true","fetch_graph":"https://pith.science/api/pith-number/AB5QGUPXP6YVOU5FX4XFFE4Z2L/graph.json","fetch_events":"https://pith.science/api/pith-number/AB5QGUPXP6YVOU5FX4XFFE4Z2L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AB5QGUPXP6YVOU5FX4XFFE4Z2L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AB5QGUPXP6YVOU5FX4XFFE4Z2L/action/storage_attestation","attest_author":"https://pith.science/pith/AB5QGUPXP6YVOU5FX4XFFE4Z2L/action/author_attestation","sign_citation":"https://pith.science/pith/AB5QGUPXP6YVOU5FX4XFFE4Z2L/action/citation_signature","submit_replication":"https://pith.science/pith/AB5QGUPXP6YVOU5FX4XFFE4Z2L/action/replication_record"}},"created_at":"2026-05-18T01:25:40.113642+00:00","updated_at":"2026-05-18T01:25:40.113642+00:00"}