{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:AFSUBPJRZBZWPKIPRN62F4DZZD","short_pith_number":"pith:AFSUBPJR","schema_version":"1.0","canonical_sha256":"016540bd31c87367a90f8b7da2f079c8c5c8e524b1ab4e0517fc01c6ecf6fc50","source":{"kind":"arxiv","id":"1508.04758","version":2},"attestation_state":"computed","paper":{"title":"Rapidly Computing Sparse Legendre Expansions via Sparse Fourier Transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Hyejin Kim, Mark Iwen, Xianfeng Hu","submitted_at":"2015-08-19T19:56:59Z","abstract_excerpt":"In this paper we propose a general strategy for rapidly computing sparse Legendre expansions. The resulting methods yield a new class of fast algorithms capable of approximating a given function $f:[-1,1] \\rightarrow \\mathbb{R}$ with a near-optimal linear combination of $s$ Legendre polynomials of degree $\\leq N$ in just $(s \\log N)^{\\mathcal{O}(1)}$-time. When $s \\ll N$ these algorithms exhibit sublinear runtime complexities in $N$, as opposed to traditional $\\Omega(N \\log N)$-time methods for computing all of the first $N$ Legendre coefficients of $f$. Theoretical as well as numerical result"},"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":"1508.04758","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-08-19T19:56:59Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"b97b8a36ef30e77f7da52824fa73b41ba6823e7592cee8668d12a292494af8b2","abstract_canon_sha256":"8a48b0a37099984c9767b11d9be25e30fd22cdaebf3abfb33dc6b4e456b7ff70"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:14.387046Z","signature_b64":"D/apV5XC80W0F2Ur1HHrHFWt1GqDpTC/JmxYmEKiTtynsYA+NC+Re3HCMRpsSMD4iMxTMITncbjc6VdTBKvqDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"016540bd31c87367a90f8b7da2f079c8c5c8e524b1ab4e0517fc01c6ecf6fc50","last_reissued_at":"2026-05-18T01:18:14.386477Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:14.386477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rapidly Computing Sparse Legendre Expansions via Sparse Fourier Transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Hyejin Kim, Mark Iwen, Xianfeng Hu","submitted_at":"2015-08-19T19:56:59Z","abstract_excerpt":"In this paper we propose a general strategy for rapidly computing sparse Legendre expansions. The resulting methods yield a new class of fast algorithms capable of approximating a given function $f:[-1,1] \\rightarrow \\mathbb{R}$ with a near-optimal linear combination of $s$ Legendre polynomials of degree $\\leq N$ in just $(s \\log N)^{\\mathcal{O}(1)}$-time. When $s \\ll N$ these algorithms exhibit sublinear runtime complexities in $N$, as opposed to traditional $\\Omega(N \\log N)$-time methods for computing all of the first $N$ Legendre coefficients of $f$. Theoretical as well as numerical result"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04758","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":"1508.04758","created_at":"2026-05-18T01:18:14.386577+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.04758v2","created_at":"2026-05-18T01:18:14.386577+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.04758","created_at":"2026-05-18T01:18:14.386577+00:00"},{"alias_kind":"pith_short_12","alias_value":"AFSUBPJRZBZW","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"AFSUBPJRZBZWPKIP","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"AFSUBPJR","created_at":"2026-05-18T12:29:10.953037+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/AFSUBPJRZBZWPKIPRN62F4DZZD","json":"https://pith.science/pith/AFSUBPJRZBZWPKIPRN62F4DZZD.json","graph_json":"https://pith.science/api/pith-number/AFSUBPJRZBZWPKIPRN62F4DZZD/graph.json","events_json":"https://pith.science/api/pith-number/AFSUBPJRZBZWPKIPRN62F4DZZD/events.json","paper":"https://pith.science/paper/AFSUBPJR"},"agent_actions":{"view_html":"https://pith.science/pith/AFSUBPJRZBZWPKIPRN62F4DZZD","download_json":"https://pith.science/pith/AFSUBPJRZBZWPKIPRN62F4DZZD.json","view_paper":"https://pith.science/paper/AFSUBPJR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.04758&json=true","fetch_graph":"https://pith.science/api/pith-number/AFSUBPJRZBZWPKIPRN62F4DZZD/graph.json","fetch_events":"https://pith.science/api/pith-number/AFSUBPJRZBZWPKIPRN62F4DZZD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AFSUBPJRZBZWPKIPRN62F4DZZD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AFSUBPJRZBZWPKIPRN62F4DZZD/action/storage_attestation","attest_author":"https://pith.science/pith/AFSUBPJRZBZWPKIPRN62F4DZZD/action/author_attestation","sign_citation":"https://pith.science/pith/AFSUBPJRZBZWPKIPRN62F4DZZD/action/citation_signature","submit_replication":"https://pith.science/pith/AFSUBPJRZBZWPKIPRN62F4DZZD/action/replication_record"}},"created_at":"2026-05-18T01:18:14.386577+00:00","updated_at":"2026-05-18T01:18:14.386577+00:00"}