{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:PNYMQJI7QMV3FWSB7XEMRRCETO","short_pith_number":"pith:PNYMQJI7","canonical_record":{"source":{"id":"1810.04504","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-10T13:16:07Z","cross_cats_sorted":[],"title_canon_sha256":"2933800a432454fa4fb2b6af705d18080eb6d22826a37567414390652033a791","abstract_canon_sha256":"0639be8487de749710ea6ff798888fdc84d95a30094d334bde2da672d1affcc1"},"schema_version":"1.0"},"canonical_sha256":"7b70c8251f832bb2da41fdc8c8c4449b9ccef2ebaa8ebb9a845c5ee1ef5bdf49","source":{"kind":"arxiv","id":"1810.04504","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.04504","created_at":"2026-05-18T00:03:39Z"},{"alias_kind":"arxiv_version","alias_value":"1810.04504v1","created_at":"2026-05-18T00:03:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.04504","created_at":"2026-05-18T00:03:39Z"},{"alias_kind":"pith_short_12","alias_value":"PNYMQJI7QMV3","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"PNYMQJI7QMV3FWSB","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"PNYMQJI7","created_at":"2026-05-18T12:32:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:PNYMQJI7QMV3FWSB7XEMRRCETO","target":"record","payload":{"canonical_record":{"source":{"id":"1810.04504","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-10T13:16:07Z","cross_cats_sorted":[],"title_canon_sha256":"2933800a432454fa4fb2b6af705d18080eb6d22826a37567414390652033a791","abstract_canon_sha256":"0639be8487de749710ea6ff798888fdc84d95a30094d334bde2da672d1affcc1"},"schema_version":"1.0"},"canonical_sha256":"7b70c8251f832bb2da41fdc8c8c4449b9ccef2ebaa8ebb9a845c5ee1ef5bdf49","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:39.969102Z","signature_b64":"oU/+aULrAuCvmyjgJS6V18pntaTK623mfVaCslnmSLQmjLCnquWPtnMvYGk6OXtKFTN9+YThtviT2OMzhxpLBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7b70c8251f832bb2da41fdc8c8c4449b9ccef2ebaa8ebb9a845c5ee1ef5bdf49","last_reissued_at":"2026-05-18T00:03:39.968487Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:39.968487Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.04504","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:03:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"293shV7bnmg/VeGYKenMu8ig29AowPlLzZK+eF649LGqsBPnUwb6vkHueAAhNSstkpuiTPpWj3guA+jOSjzoDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T16:36:51.000771Z"},"content_sha256":"b1a1842016b6cc6e45598dd17f4d1cb4253260ec643c1a95d078da4e6e5e3fa4","schema_version":"1.0","event_id":"sha256:b1a1842016b6cc6e45598dd17f4d1cb4253260ec643c1a95d078da4e6e5e3fa4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:PNYMQJI7QMV3FWSB7XEMRRCETO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Randomized Method of Subspace Corrections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Jinchao Xu, Ludmil Zikatanov, Xiaozhe Hu","submitted_at":"2018-10-10T13:16:07Z","abstract_excerpt":"In this paper, we consider the iterative method of subspace corrections with random ordering. We prove identities for the expected convergence rate, which can provide sharp estimates for the error reduction per iteration. We also study the fault-tolerant feature of the randomized successive subspace correction method by simply rejecting all the corrections when error occurs and show that the results iterative method converges with probability one. Moreover, we also provide sharp estimates on the expected convergence rate for the fault-tolerant, randomized, subspace correction method."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04504","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:03:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q0IhtzquNCLwIPN+6XByuutcrgl+hGl1DA/d/XiUaKvN1MtdYwxYDOqLOhvXkg2rz86KDTJBS3dTUhXuC5UJAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T16:36:51.001418Z"},"content_sha256":"56b46c7847d897ca74f393be6b31a3b4da90907f02e96a3b361fc77b4c04e94d","schema_version":"1.0","event_id":"sha256:56b46c7847d897ca74f393be6b31a3b4da90907f02e96a3b361fc77b4c04e94d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PNYMQJI7QMV3FWSB7XEMRRCETO/bundle.json","state_url":"https://pith.science/pith/PNYMQJI7QMV3FWSB7XEMRRCETO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PNYMQJI7QMV3FWSB7XEMRRCETO/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":"2026-05-29T16:36:51Z","links":{"resolver":"https://pith.science/pith/PNYMQJI7QMV3FWSB7XEMRRCETO","bundle":"https://pith.science/pith/PNYMQJI7QMV3FWSB7XEMRRCETO/bundle.json","state":"https://pith.science/pith/PNYMQJI7QMV3FWSB7XEMRRCETO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PNYMQJI7QMV3FWSB7XEMRRCETO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:PNYMQJI7QMV3FWSB7XEMRRCETO","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":"0639be8487de749710ea6ff798888fdc84d95a30094d334bde2da672d1affcc1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-10T13:16:07Z","title_canon_sha256":"2933800a432454fa4fb2b6af705d18080eb6d22826a37567414390652033a791"},"schema_version":"1.0","source":{"id":"1810.04504","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.04504","created_at":"2026-05-18T00:03:39Z"},{"alias_kind":"arxiv_version","alias_value":"1810.04504v1","created_at":"2026-05-18T00:03:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.04504","created_at":"2026-05-18T00:03:39Z"},{"alias_kind":"pith_short_12","alias_value":"PNYMQJI7QMV3","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"PNYMQJI7QMV3FWSB","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"PNYMQJI7","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:56b46c7847d897ca74f393be6b31a3b4da90907f02e96a3b361fc77b4c04e94d","target":"graph","created_at":"2026-05-18T00:03:39Z","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"},"paper":{"abstract_excerpt":"In this paper, we consider the iterative method of subspace corrections with random ordering. We prove identities for the expected convergence rate, which can provide sharp estimates for the error reduction per iteration. We also study the fault-tolerant feature of the randomized successive subspace correction method by simply rejecting all the corrections when error occurs and show that the results iterative method converges with probability one. Moreover, we also provide sharp estimates on the expected convergence rate for the fault-tolerant, randomized, subspace correction method.","authors_text":"Jinchao Xu, Ludmil Zikatanov, Xiaozhe Hu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-10T13:16:07Z","title":"Randomized Method of Subspace Corrections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04504","kind":"arxiv","version":1},"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:b1a1842016b6cc6e45598dd17f4d1cb4253260ec643c1a95d078da4e6e5e3fa4","target":"record","created_at":"2026-05-18T00:03:39Z","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":"0639be8487de749710ea6ff798888fdc84d95a30094d334bde2da672d1affcc1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-10T13:16:07Z","title_canon_sha256":"2933800a432454fa4fb2b6af705d18080eb6d22826a37567414390652033a791"},"schema_version":"1.0","source":{"id":"1810.04504","kind":"arxiv","version":1}},"canonical_sha256":"7b70c8251f832bb2da41fdc8c8c4449b9ccef2ebaa8ebb9a845c5ee1ef5bdf49","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7b70c8251f832bb2da41fdc8c8c4449b9ccef2ebaa8ebb9a845c5ee1ef5bdf49","first_computed_at":"2026-05-18T00:03:39.968487Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:39.968487Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oU/+aULrAuCvmyjgJS6V18pntaTK623mfVaCslnmSLQmjLCnquWPtnMvYGk6OXtKFTN9+YThtviT2OMzhxpLBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:39.969102Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.04504","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b1a1842016b6cc6e45598dd17f4d1cb4253260ec643c1a95d078da4e6e5e3fa4","sha256:56b46c7847d897ca74f393be6b31a3b4da90907f02e96a3b361fc77b4c04e94d"],"state_sha256":"ea6295b3c9b4c191721c6c5eb843bf50d6aec28b4b7cf45d0622cb27d1276f97"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NLGJQf2o4v0MNEZ+4nWFi4xh3x5bLti6ZD1x9CFEYSOWyL+9s4re4DKHkw35yJfOoxFnn/RMb/l/EosRCljZAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T16:36:51.004769Z","bundle_sha256":"703b263d68173586bcdf9497f30b2a1e7c39ada66c87ba897cac9ead7aca0121"}}