{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:RN63E3SAIT3LQSS4CW3TJYPIRN","short_pith_number":"pith:RN63E3SA","schema_version":"1.0","canonical_sha256":"8b7db26e4044f6b84a5c15b734e1e88b7909fcccfe703490027fcd4253a2bb25","source":{"kind":"arxiv","id":"1204.0062","version":4},"attestation_state":"computed","paper":{"title":"Improved matrix algorithms via the Subsampled Randomized Hadamard Transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"cs.DS","authors_text":"Alex Gittens, Christos Boutsidis","submitted_at":"2012-03-31T02:49:46Z","abstract_excerpt":"Several recent randomized linear algebra algorithms rely upon fast dimension reduction methods. A popular choice is the Subsampled Randomized Hadamard Transform (SRHT). In this article, we address the efficacy, in the Frobenius and spectral norms, of an SRHT-based low-rank matrix approximation technique introduced by Woolfe, Liberty, Rohklin, and Tygert. We establish a slightly better Frobenius norm error bound than currently available, and a much sharper spectral norm error bound (in the presence of reasonable decay of the singular values). Along the way, we produce several results on matrix "},"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":"1204.0062","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-03-31T02:49:46Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"f3ae8a0bdafb5b277597693d6b5f4a59f1bf3e170f0a16143cb8c3e3f17c1d32","abstract_canon_sha256":"9130e6f3f6890f513f86076b49ecc74c052e54df208b540ee0d10669034108c3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:21:16.707053Z","signature_b64":"vjIK9tgrldv0JIu8NdZqrgRj5o6Rm6sXjEi3QsmT2ycDquEABWb3J9v8f4Jo9DNgOyku8WSU2Jl/e7qKkDE/BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8b7db26e4044f6b84a5c15b734e1e88b7909fcccfe703490027fcd4253a2bb25","last_reissued_at":"2026-05-18T02:21:16.706400Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:21:16.706400Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Improved matrix algorithms via the Subsampled Randomized Hadamard Transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"cs.DS","authors_text":"Alex Gittens, Christos Boutsidis","submitted_at":"2012-03-31T02:49:46Z","abstract_excerpt":"Several recent randomized linear algebra algorithms rely upon fast dimension reduction methods. A popular choice is the Subsampled Randomized Hadamard Transform (SRHT). In this article, we address the efficacy, in the Frobenius and spectral norms, of an SRHT-based low-rank matrix approximation technique introduced by Woolfe, Liberty, Rohklin, and Tygert. We establish a slightly better Frobenius norm error bound than currently available, and a much sharper spectral norm error bound (in the presence of reasonable decay of the singular values). Along the way, we produce several results on matrix "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.0062","kind":"arxiv","version":4},"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":"1204.0062","created_at":"2026-05-18T02:21:16.706506+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.0062v4","created_at":"2026-05-18T02:21:16.706506+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.0062","created_at":"2026-05-18T02:21:16.706506+00:00"},{"alias_kind":"pith_short_12","alias_value":"RN63E3SAIT3L","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_16","alias_value":"RN63E3SAIT3LQSS4","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_8","alias_value":"RN63E3SA","created_at":"2026-05-18T12:27:20.899486+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/RN63E3SAIT3LQSS4CW3TJYPIRN","json":"https://pith.science/pith/RN63E3SAIT3LQSS4CW3TJYPIRN.json","graph_json":"https://pith.science/api/pith-number/RN63E3SAIT3LQSS4CW3TJYPIRN/graph.json","events_json":"https://pith.science/api/pith-number/RN63E3SAIT3LQSS4CW3TJYPIRN/events.json","paper":"https://pith.science/paper/RN63E3SA"},"agent_actions":{"view_html":"https://pith.science/pith/RN63E3SAIT3LQSS4CW3TJYPIRN","download_json":"https://pith.science/pith/RN63E3SAIT3LQSS4CW3TJYPIRN.json","view_paper":"https://pith.science/paper/RN63E3SA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.0062&json=true","fetch_graph":"https://pith.science/api/pith-number/RN63E3SAIT3LQSS4CW3TJYPIRN/graph.json","fetch_events":"https://pith.science/api/pith-number/RN63E3SAIT3LQSS4CW3TJYPIRN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RN63E3SAIT3LQSS4CW3TJYPIRN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RN63E3SAIT3LQSS4CW3TJYPIRN/action/storage_attestation","attest_author":"https://pith.science/pith/RN63E3SAIT3LQSS4CW3TJYPIRN/action/author_attestation","sign_citation":"https://pith.science/pith/RN63E3SAIT3LQSS4CW3TJYPIRN/action/citation_signature","submit_replication":"https://pith.science/pith/RN63E3SAIT3LQSS4CW3TJYPIRN/action/replication_record"}},"created_at":"2026-05-18T02:21:16.706506+00:00","updated_at":"2026-05-18T02:21:16.706506+00:00"}