{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:6WEPGC75E37PA2FX2FCQOQPGNN","short_pith_number":"pith:6WEPGC75","canonical_record":{"source":{"id":"1807.08419","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-07-23T03:41:44Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"e40d1c842c964bd0f678c47640bb9bb00ba30d3e06cc0cf2d5d706dc74aa7773","abstract_canon_sha256":"d39f597bdb896e37541d31d0778060a53e8fc2c8addcc5fb12b3f0fd2f5b6553"},"schema_version":"1.0"},"canonical_sha256":"f588f30bfd26fef068b7d1450741e66b59d51b0f01a800c64485d180a27e630f","source":{"kind":"arxiv","id":"1807.08419","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.08419","created_at":"2026-06-04T19:12:08Z"},{"alias_kind":"arxiv_version","alias_value":"1807.08419v2","created_at":"2026-06-04T19:12:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.08419","created_at":"2026-06-04T19:12:08Z"},{"alias_kind":"pith_short_12","alias_value":"6WEPGC75E37P","created_at":"2026-06-04T19:12:08Z"},{"alias_kind":"pith_short_16","alias_value":"6WEPGC75E37PA2FX","created_at":"2026-06-04T19:12:08Z"},{"alias_kind":"pith_short_8","alias_value":"6WEPGC75","created_at":"2026-06-04T19:12:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:6WEPGC75E37PA2FX2FCQOQPGNN","target":"record","payload":{"canonical_record":{"source":{"id":"1807.08419","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-07-23T03:41:44Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"e40d1c842c964bd0f678c47640bb9bb00ba30d3e06cc0cf2d5d706dc74aa7773","abstract_canon_sha256":"d39f597bdb896e37541d31d0778060a53e8fc2c8addcc5fb12b3f0fd2f5b6553"},"schema_version":"1.0"},"canonical_sha256":"f588f30bfd26fef068b7d1450741e66b59d51b0f01a800c64485d180a27e630f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T19:12:08.760589Z","signature_b64":"44wQGuXdnGOifF17W6/CVIaOnUBKvTX+T4CwttsEjZqufXTkyxUbR50Dl5iL1dGz5mGq8R8ZEw1J/ajPXwFABQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f588f30bfd26fef068b7d1450741e66b59d51b0f01a800c64485d180a27e630f","last_reissued_at":"2026-06-04T19:12:08.760070Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T19:12:08.760070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.08419","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-04T19:12:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"muQEt9DiFa+zkOUv9S2AIUG6WBsDu4FGxvc7rU7O8N81oMTLZbaPHHzY97RQfiFWSruCI6YExu+InuCZXxskBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T22:46:24.530129Z"},"content_sha256":"6c11fb74ee3a59dad5962e6c0f295f3d76fb495d38adacad91873116f917a0a7","schema_version":"1.0","event_id":"sha256:6c11fb74ee3a59dad5962e6c0f295f3d76fb495d38adacad91873116f917a0a7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:6WEPGC75E37PA2FX2FCQOQPGNN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Joint Bidiagonalization Based Algorithm for Large Scale Linear Discrete Ill-posed Problems in General-Form Regularization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Yanfei Yang, Zhongxiao Jia","submitted_at":"2018-07-23T03:41:44Z","abstract_excerpt":"Based on the joint bidiagonalization process of a large matrix pair $\\{A,L\\}$, we propose and develop an iterative regularization algorithm for the large scale linear discrete ill-posed problems in general-form regularization: $\\min\\|Lx\\| \\ \\mbox{{\\rm subject to}} \\ x\\in\\mathcal{S} = \\{x|\\ \\|Ax-b\\|\\leq \\tau\\|e\\|\\}$ with a Gaussian white noise $e$ and $\\tau>1$ slightly, where $L$ is a regularization matrix. Our algorithm is different from the hybrid one proposed by Kilmer {\\em et al.}, which is based on the same process but solves the general-form Tikhonov regularization problem: $\\min_x\\left\\{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.08419","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1807.08419/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-04T19:12:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hceWa3Xy7Q1uuUHJaDFcQI4Ju6IZ/y/cIdsf3QM8FEjt02dIvV1D0IY+LaaBHQ/JFexc5y9brNRKOpg+bkWICQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T22:46:24.530528Z"},"content_sha256":"4dd87525e3f3a8ef4d67eae0b123bf740d799abc999df80f0637932484d0783f","schema_version":"1.0","event_id":"sha256:4dd87525e3f3a8ef4d67eae0b123bf740d799abc999df80f0637932484d0783f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6WEPGC75E37PA2FX2FCQOQPGNN/bundle.json","state_url":"https://pith.science/pith/6WEPGC75E37PA2FX2FCQOQPGNN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6WEPGC75E37PA2FX2FCQOQPGNN/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-20T22:46:24Z","links":{"resolver":"https://pith.science/pith/6WEPGC75E37PA2FX2FCQOQPGNN","bundle":"https://pith.science/pith/6WEPGC75E37PA2FX2FCQOQPGNN/bundle.json","state":"https://pith.science/pith/6WEPGC75E37PA2FX2FCQOQPGNN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6WEPGC75E37PA2FX2FCQOQPGNN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6WEPGC75E37PA2FX2FCQOQPGNN","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d39f597bdb896e37541d31d0778060a53e8fc2c8addcc5fb12b3f0fd2f5b6553","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-07-23T03:41:44Z","title_canon_sha256":"e40d1c842c964bd0f678c47640bb9bb00ba30d3e06cc0cf2d5d706dc74aa7773"},"schema_version":"1.0","source":{"id":"1807.08419","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.08419","created_at":"2026-06-04T19:12:08Z"},{"alias_kind":"arxiv_version","alias_value":"1807.08419v2","created_at":"2026-06-04T19:12:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.08419","created_at":"2026-06-04T19:12:08Z"},{"alias_kind":"pith_short_12","alias_value":"6WEPGC75E37P","created_at":"2026-06-04T19:12:08Z"},{"alias_kind":"pith_short_16","alias_value":"6WEPGC75E37PA2FX","created_at":"2026-06-04T19:12:08Z"},{"alias_kind":"pith_short_8","alias_value":"6WEPGC75","created_at":"2026-06-04T19:12:08Z"}],"graph_snapshots":[{"event_id":"sha256:4dd87525e3f3a8ef4d67eae0b123bf740d799abc999df80f0637932484d0783f","target":"graph","created_at":"2026-06-04T19:12:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1807.08419/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Based on the joint bidiagonalization process of a large matrix pair $\\{A,L\\}$, we propose and develop an iterative regularization algorithm for the large scale linear discrete ill-posed problems in general-form regularization: $\\min\\|Lx\\| \\ \\mbox{{\\rm subject to}} \\ x\\in\\mathcal{S} = \\{x|\\ \\|Ax-b\\|\\leq \\tau\\|e\\|\\}$ with a Gaussian white noise $e$ and $\\tau>1$ slightly, where $L$ is a regularization matrix. Our algorithm is different from the hybrid one proposed by Kilmer {\\em et al.}, which is based on the same process but solves the general-form Tikhonov regularization problem: $\\min_x\\left\\{","authors_text":"Yanfei Yang, Zhongxiao Jia","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-07-23T03:41:44Z","title":"A Joint Bidiagonalization Based Algorithm for Large Scale Linear Discrete Ill-posed Problems in General-Form Regularization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.08419","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6c11fb74ee3a59dad5962e6c0f295f3d76fb495d38adacad91873116f917a0a7","target":"record","created_at":"2026-06-04T19:12:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d39f597bdb896e37541d31d0778060a53e8fc2c8addcc5fb12b3f0fd2f5b6553","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-07-23T03:41:44Z","title_canon_sha256":"e40d1c842c964bd0f678c47640bb9bb00ba30d3e06cc0cf2d5d706dc74aa7773"},"schema_version":"1.0","source":{"id":"1807.08419","kind":"arxiv","version":2}},"canonical_sha256":"f588f30bfd26fef068b7d1450741e66b59d51b0f01a800c64485d180a27e630f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f588f30bfd26fef068b7d1450741e66b59d51b0f01a800c64485d180a27e630f","first_computed_at":"2026-06-04T19:12:08.760070Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T19:12:08.760070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"44wQGuXdnGOifF17W6/CVIaOnUBKvTX+T4CwttsEjZqufXTkyxUbR50Dl5iL1dGz5mGq8R8ZEw1J/ajPXwFABQ==","signature_status":"signed_v1","signed_at":"2026-06-04T19:12:08.760589Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.08419","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c11fb74ee3a59dad5962e6c0f295f3d76fb495d38adacad91873116f917a0a7","sha256:4dd87525e3f3a8ef4d67eae0b123bf740d799abc999df80f0637932484d0783f"],"state_sha256":"cea1fb69b0586fdb3871f123daabbdd4afe06dd4dc9ec3c212adee6033652eb1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"erDjF1BPvzax63dHbfRwhFz0+IM0XAZVWBXZRTV4u2kpdQUl83doQlLyUpQGfrfKL7rm/TblPt9C01ukoZCYCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T22:46:24.532471Z","bundle_sha256":"801948120363f6fa1f7228697637f38c6e3d6e82759e6014a2fef530b6b6c8d5"}}