{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:VRFWEDJWH72LYXGFETB5IGFK4V","short_pith_number":"pith:VRFWEDJW","schema_version":"1.0","canonical_sha256":"ac4b620d363ff4bc5cc524c3d418aae57c150449032285b73fff5299032940af","source":{"kind":"arxiv","id":"1511.03186","version":2},"attestation_state":"computed","paper":{"title":"Accelerated Newton Iteration: Roots of Black Box Polynomials and Matrix Eigenvalues","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Anand Louis, Santosh S. Vempala","submitted_at":"2015-11-10T17:07:35Z","abstract_excerpt":"We study the problem of computing the largest root of a real rooted polynomial $p(x)$ to within error $\\varepsilon $ given only black box access to it, i.e., for any $x \\in {\\mathbb R}$, the algorithm can query an oracle for the value of $p(x)$, but the algorithm is not allowed access to the coefficients of $p(x)$. A folklore result for this problem is that the largest root of a polynomial can be computed in $O(n \\log (1/\\varepsilon ))$ polynomial queries using the Newton iteration. We give a simple algorithm that queries the oracle at only $O(\\log n \\log(1/\\varepsilon ))$ points, where $n$ is"},"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":"1511.03186","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-11-10T17:07:35Z","cross_cats_sorted":[],"title_canon_sha256":"f0c7e107c255fa7b0a439f0f4d71eee0956e8cbd0cc809a47c7391f624dd6fc9","abstract_canon_sha256":"fba8887848edda7419391ac140cf96aa0f095c3d55335e8026ac9dbd47296435"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:28.709598Z","signature_b64":"fR9KIJ//GQ/KwEskpkSLQVKHZtMHX9wAfMMZ187MITbcpFHOAAPOttbylmoutQEDdVrHyWfo3p/9B1PHwmZuAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac4b620d363ff4bc5cc524c3d418aae57c150449032285b73fff5299032940af","last_reissued_at":"2026-05-18T01:23:28.708893Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:28.708893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Accelerated Newton Iteration: Roots of Black Box Polynomials and Matrix Eigenvalues","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Anand Louis, Santosh S. Vempala","submitted_at":"2015-11-10T17:07:35Z","abstract_excerpt":"We study the problem of computing the largest root of a real rooted polynomial $p(x)$ to within error $\\varepsilon $ given only black box access to it, i.e., for any $x \\in {\\mathbb R}$, the algorithm can query an oracle for the value of $p(x)$, but the algorithm is not allowed access to the coefficients of $p(x)$. A folklore result for this problem is that the largest root of a polynomial can be computed in $O(n \\log (1/\\varepsilon ))$ polynomial queries using the Newton iteration. We give a simple algorithm that queries the oracle at only $O(\\log n \\log(1/\\varepsilon ))$ points, where $n$ is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03186","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":"1511.03186","created_at":"2026-05-18T01:23:28.709004+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.03186v2","created_at":"2026-05-18T01:23:28.709004+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.03186","created_at":"2026-05-18T01:23:28.709004+00:00"},{"alias_kind":"pith_short_12","alias_value":"VRFWEDJWH72L","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_16","alias_value":"VRFWEDJWH72LYXGF","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_8","alias_value":"VRFWEDJW","created_at":"2026-05-18T12:29:47.479230+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/VRFWEDJWH72LYXGFETB5IGFK4V","json":"https://pith.science/pith/VRFWEDJWH72LYXGFETB5IGFK4V.json","graph_json":"https://pith.science/api/pith-number/VRFWEDJWH72LYXGFETB5IGFK4V/graph.json","events_json":"https://pith.science/api/pith-number/VRFWEDJWH72LYXGFETB5IGFK4V/events.json","paper":"https://pith.science/paper/VRFWEDJW"},"agent_actions":{"view_html":"https://pith.science/pith/VRFWEDJWH72LYXGFETB5IGFK4V","download_json":"https://pith.science/pith/VRFWEDJWH72LYXGFETB5IGFK4V.json","view_paper":"https://pith.science/paper/VRFWEDJW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.03186&json=true","fetch_graph":"https://pith.science/api/pith-number/VRFWEDJWH72LYXGFETB5IGFK4V/graph.json","fetch_events":"https://pith.science/api/pith-number/VRFWEDJWH72LYXGFETB5IGFK4V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VRFWEDJWH72LYXGFETB5IGFK4V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VRFWEDJWH72LYXGFETB5IGFK4V/action/storage_attestation","attest_author":"https://pith.science/pith/VRFWEDJWH72LYXGFETB5IGFK4V/action/author_attestation","sign_citation":"https://pith.science/pith/VRFWEDJWH72LYXGFETB5IGFK4V/action/citation_signature","submit_replication":"https://pith.science/pith/VRFWEDJWH72LYXGFETB5IGFK4V/action/replication_record"}},"created_at":"2026-05-18T01:23:28.709004+00:00","updated_at":"2026-05-18T01:23:28.709004+00:00"}