{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:AKIXTYHE5XNREZB523OHBOJ3CU","short_pith_number":"pith:AKIXTYHE","schema_version":"1.0","canonical_sha256":"029179e0e4eddb12643dd6dc70b93b151ac41a9295c875978af594ba7572eab7","source":{"kind":"arxiv","id":"1712.06645","version":2},"attestation_state":"computed","paper":{"title":"Compressive Hermite interpolation: sparse, high-dimensional approximation from gradient-augmented measurements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.NA","authors_text":"Ben Adcock, Yi Sui","submitted_at":"2017-12-18T19:45:35Z","abstract_excerpt":"We consider the sparse polynomial approximation of a multivariate function on a tensor product domain from samples of both the function and its gradient. When only function samples are prescribed, weighted $\\ell^1$ minimization has recently been shown to be an effective procedure for computing such approximations. We extend this work to the gradient-augmented case. Our main results show that for the same asymptotic sample complexity, gradient-augmented measurements achieve an approximation error bound in a stronger Sobolev norm, as opposed to the $L^2$-norm in the unaugmented case. For Chebysh"},"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":"1712.06645","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-12-18T19:45:35Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"094ad8b0678136efac02cb99c9f47c94dc47beb8c3637a1fbdead048f1f7fd3b","abstract_canon_sha256":"cffb62db2e59ee39b2eea32fd52957ce003365f37b78b1c3f5a6546a2132fc31"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:06.711818Z","signature_b64":"KFMd3r4cWilGNE8FEQ3O+bGT93l8tIm0gyUO36x/TXrD5m+yLpmXwTvF9x6QCRDlKNLxCZ6d9f1VGDKDF/lRBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"029179e0e4eddb12643dd6dc70b93b151ac41a9295c875978af594ba7572eab7","last_reissued_at":"2026-05-17T23:53:06.711167Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:06.711167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Compressive Hermite interpolation: sparse, high-dimensional approximation from gradient-augmented measurements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.NA","authors_text":"Ben Adcock, Yi Sui","submitted_at":"2017-12-18T19:45:35Z","abstract_excerpt":"We consider the sparse polynomial approximation of a multivariate function on a tensor product domain from samples of both the function and its gradient. When only function samples are prescribed, weighted $\\ell^1$ minimization has recently been shown to be an effective procedure for computing such approximations. We extend this work to the gradient-augmented case. Our main results show that for the same asymptotic sample complexity, gradient-augmented measurements achieve an approximation error bound in a stronger Sobolev norm, as opposed to the $L^2$-norm in the unaugmented case. For Chebysh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.06645","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":"1712.06645","created_at":"2026-05-17T23:53:06.711282+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.06645v2","created_at":"2026-05-17T23:53:06.711282+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.06645","created_at":"2026-05-17T23:53:06.711282+00:00"},{"alias_kind":"pith_short_12","alias_value":"AKIXTYHE5XNR","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_16","alias_value":"AKIXTYHE5XNREZB5","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_8","alias_value":"AKIXTYHE","created_at":"2026-05-18T12:31:05.417338+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/AKIXTYHE5XNREZB523OHBOJ3CU","json":"https://pith.science/pith/AKIXTYHE5XNREZB523OHBOJ3CU.json","graph_json":"https://pith.science/api/pith-number/AKIXTYHE5XNREZB523OHBOJ3CU/graph.json","events_json":"https://pith.science/api/pith-number/AKIXTYHE5XNREZB523OHBOJ3CU/events.json","paper":"https://pith.science/paper/AKIXTYHE"},"agent_actions":{"view_html":"https://pith.science/pith/AKIXTYHE5XNREZB523OHBOJ3CU","download_json":"https://pith.science/pith/AKIXTYHE5XNREZB523OHBOJ3CU.json","view_paper":"https://pith.science/paper/AKIXTYHE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.06645&json=true","fetch_graph":"https://pith.science/api/pith-number/AKIXTYHE5XNREZB523OHBOJ3CU/graph.json","fetch_events":"https://pith.science/api/pith-number/AKIXTYHE5XNREZB523OHBOJ3CU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AKIXTYHE5XNREZB523OHBOJ3CU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AKIXTYHE5XNREZB523OHBOJ3CU/action/storage_attestation","attest_author":"https://pith.science/pith/AKIXTYHE5XNREZB523OHBOJ3CU/action/author_attestation","sign_citation":"https://pith.science/pith/AKIXTYHE5XNREZB523OHBOJ3CU/action/citation_signature","submit_replication":"https://pith.science/pith/AKIXTYHE5XNREZB523OHBOJ3CU/action/replication_record"}},"created_at":"2026-05-17T23:53:06.711282+00:00","updated_at":"2026-05-17T23:53:06.711282+00:00"}