{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:74D6JX5K7ROSG7E5KFARLWB5HV","short_pith_number":"pith:74D6JX5K","schema_version":"1.0","canonical_sha256":"ff07e4dfaafc5d237c9d514115d83d3d4f42005c007a165013b79a56a03450e9","source":{"kind":"arxiv","id":"1707.04200","version":1},"attestation_state":"computed","paper":{"title":"Stopping criterion for iterative regularization of large-scale ill-posed problems using the Picard parameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Alexander Y. Meltzer, Eitan Levin","submitted_at":"2017-07-13T16:22:13Z","abstract_excerpt":"We propose a new stopping criterion for Krylov subspace iterative regularization of large-scale ill-posed inverse problems. Our stopping criterion accurately filters the data using a generalization of the Picard parameter that was originally introduced for direct regularization of small-scale problems. In the one dimension we filter the data in the discrete Fourier transform (DFT) basis using the Picard parameter, which separates noise-dominated Fourier coefficients from the signal-dominated ones. For two-dimensional problems we propose a novel vectorization scheme of the Fourier coefficients "},"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":"1707.04200","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-07-13T16:22:13Z","cross_cats_sorted":[],"title_canon_sha256":"7e88acb14cf937e29e56636bce396339a21701535020968546c9bfa16fc2eb4b","abstract_canon_sha256":"f20998faced24754155947694c4b0b897459fde6b319b863855dc96deb9e4345"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:20.253639Z","signature_b64":"bWG0dtjbgK3f6SSScGsjK4c2ejer3L84DlWd1A2e8E7W0ZXKifbiDpC6bocwTDHsPl+B3qchUSezMgu5UrBDAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff07e4dfaafc5d237c9d514115d83d3d4f42005c007a165013b79a56a03450e9","last_reissued_at":"2026-05-18T00:40:20.252962Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:20.252962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stopping criterion for iterative regularization of large-scale ill-posed problems using the Picard parameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Alexander Y. Meltzer, Eitan Levin","submitted_at":"2017-07-13T16:22:13Z","abstract_excerpt":"We propose a new stopping criterion for Krylov subspace iterative regularization of large-scale ill-posed inverse problems. Our stopping criterion accurately filters the data using a generalization of the Picard parameter that was originally introduced for direct regularization of small-scale problems. In the one dimension we filter the data in the discrete Fourier transform (DFT) basis using the Picard parameter, which separates noise-dominated Fourier coefficients from the signal-dominated ones. For two-dimensional problems we propose a novel vectorization scheme of the Fourier coefficients "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.04200","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":"1707.04200","created_at":"2026-05-18T00:40:20.253063+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.04200v1","created_at":"2026-05-18T00:40:20.253063+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.04200","created_at":"2026-05-18T00:40:20.253063+00:00"},{"alias_kind":"pith_short_12","alias_value":"74D6JX5K7ROS","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_16","alias_value":"74D6JX5K7ROSG7E5","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_8","alias_value":"74D6JX5K","created_at":"2026-05-18T12:31:03.183658+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/74D6JX5K7ROSG7E5KFARLWB5HV","json":"https://pith.science/pith/74D6JX5K7ROSG7E5KFARLWB5HV.json","graph_json":"https://pith.science/api/pith-number/74D6JX5K7ROSG7E5KFARLWB5HV/graph.json","events_json":"https://pith.science/api/pith-number/74D6JX5K7ROSG7E5KFARLWB5HV/events.json","paper":"https://pith.science/paper/74D6JX5K"},"agent_actions":{"view_html":"https://pith.science/pith/74D6JX5K7ROSG7E5KFARLWB5HV","download_json":"https://pith.science/pith/74D6JX5K7ROSG7E5KFARLWB5HV.json","view_paper":"https://pith.science/paper/74D6JX5K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.04200&json=true","fetch_graph":"https://pith.science/api/pith-number/74D6JX5K7ROSG7E5KFARLWB5HV/graph.json","fetch_events":"https://pith.science/api/pith-number/74D6JX5K7ROSG7E5KFARLWB5HV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/74D6JX5K7ROSG7E5KFARLWB5HV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/74D6JX5K7ROSG7E5KFARLWB5HV/action/storage_attestation","attest_author":"https://pith.science/pith/74D6JX5K7ROSG7E5KFARLWB5HV/action/author_attestation","sign_citation":"https://pith.science/pith/74D6JX5K7ROSG7E5KFARLWB5HV/action/citation_signature","submit_replication":"https://pith.science/pith/74D6JX5K7ROSG7E5KFARLWB5HV/action/replication_record"}},"created_at":"2026-05-18T00:40:20.253063+00:00","updated_at":"2026-05-18T00:40:20.253063+00:00"}