{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:Y7SGV4R2TVO2WXMCWC6O3VQIZM","short_pith_number":"pith:Y7SGV4R2","schema_version":"1.0","canonical_sha256":"c7e46af23a9d5dab5d82b0bcedd608cb151192958a63185ebd300f5de4ceb35e","source":{"kind":"arxiv","id":"1706.00092","version":1},"attestation_state":"computed","paper":{"title":"Inexact Gradient Projection and Fast Data Driven Compressed Sensing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Mike E. Davies, Mohammad Golbabaee","submitted_at":"2017-05-31T21:14:32Z","abstract_excerpt":"We study convergence of the iterative projected gradient (IPG) algorithm for arbitrary (possibly nonconvex) sets and when both the gradient and projection oracles are computed approximately. We consider different notions of approximation of which we show that the Progressive Fixed Precision (PFP) and the $(1+\\epsilon)$-optimal oracles can achieve the same accuracy as for the exact IPG algorithm. We show that the former scheme is also able to maintain the (linear) rate of convergence of the exact algorithm, under the same embedding assumption. In contrast, the $(1+\\epsilon)$-approximate oracle "},"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":"1706.00092","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-05-31T21:14:32Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"b314d13366e3b3eb478298f162db0981cb29a11e50e0fdad6067b895e8ae0be6","abstract_canon_sha256":"9b3505cd69e931c9b2152b77f1d0071b30c7cc77eaa3c36125ecf0caf4c77041"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:15.057533Z","signature_b64":"Z3093VAZHN7ZynDae1vxdNwLS9W5IYTm29UnanIl/S4bAB7ng9RgAjhYszq7ycA3mBeXnoPYL5yZ1bLOyZzmAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c7e46af23a9d5dab5d82b0bcedd608cb151192958a63185ebd300f5de4ceb35e","last_reissued_at":"2026-05-18T00:43:15.056996Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:15.056996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Inexact Gradient Projection and Fast Data Driven Compressed Sensing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Mike E. Davies, Mohammad Golbabaee","submitted_at":"2017-05-31T21:14:32Z","abstract_excerpt":"We study convergence of the iterative projected gradient (IPG) algorithm for arbitrary (possibly nonconvex) sets and when both the gradient and projection oracles are computed approximately. We consider different notions of approximation of which we show that the Progressive Fixed Precision (PFP) and the $(1+\\epsilon)$-optimal oracles can achieve the same accuracy as for the exact IPG algorithm. We show that the former scheme is also able to maintain the (linear) rate of convergence of the exact algorithm, under the same embedding assumption. In contrast, the $(1+\\epsilon)$-approximate oracle "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00092","kind":"arxiv","version":1},"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":"1706.00092","created_at":"2026-05-18T00:43:15.057076+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.00092v1","created_at":"2026-05-18T00:43:15.057076+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.00092","created_at":"2026-05-18T00:43:15.057076+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y7SGV4R2TVO2","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y7SGV4R2TVO2WXMC","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y7SGV4R2","created_at":"2026-05-18T12:31:56.362134+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/Y7SGV4R2TVO2WXMCWC6O3VQIZM","json":"https://pith.science/pith/Y7SGV4R2TVO2WXMCWC6O3VQIZM.json","graph_json":"https://pith.science/api/pith-number/Y7SGV4R2TVO2WXMCWC6O3VQIZM/graph.json","events_json":"https://pith.science/api/pith-number/Y7SGV4R2TVO2WXMCWC6O3VQIZM/events.json","paper":"https://pith.science/paper/Y7SGV4R2"},"agent_actions":{"view_html":"https://pith.science/pith/Y7SGV4R2TVO2WXMCWC6O3VQIZM","download_json":"https://pith.science/pith/Y7SGV4R2TVO2WXMCWC6O3VQIZM.json","view_paper":"https://pith.science/paper/Y7SGV4R2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.00092&json=true","fetch_graph":"https://pith.science/api/pith-number/Y7SGV4R2TVO2WXMCWC6O3VQIZM/graph.json","fetch_events":"https://pith.science/api/pith-number/Y7SGV4R2TVO2WXMCWC6O3VQIZM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y7SGV4R2TVO2WXMCWC6O3VQIZM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y7SGV4R2TVO2WXMCWC6O3VQIZM/action/storage_attestation","attest_author":"https://pith.science/pith/Y7SGV4R2TVO2WXMCWC6O3VQIZM/action/author_attestation","sign_citation":"https://pith.science/pith/Y7SGV4R2TVO2WXMCWC6O3VQIZM/action/citation_signature","submit_replication":"https://pith.science/pith/Y7SGV4R2TVO2WXMCWC6O3VQIZM/action/replication_record"}},"created_at":"2026-05-18T00:43:15.057076+00:00","updated_at":"2026-05-18T00:43:15.057076+00:00"}