{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:7ZKVA3ZKIL3GFCOH6YL6WFRYRJ","short_pith_number":"pith:7ZKVA3ZK","canonical_record":{"source":{"id":"1302.0196","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-02-01T14:57:40Z","cross_cats_sorted":[],"title_canon_sha256":"8d56e8d6671a55d5a53efc7a65f4ba23e2ea735a51a55cfa38ccbdb8cd5e7eea","abstract_canon_sha256":"a48843632c4fb6b18d73e76b125fcc8c5ef918856ea26c38bb0f269bfaf3b520"},"schema_version":"1.0"},"canonical_sha256":"fe55506f2a42f66289c7f617eb16388a5ecc1fbfe91c2dc61cd358cb895ec3ff","source":{"kind":"arxiv","id":"1302.0196","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.0196","created_at":"2026-05-18T03:34:47Z"},{"alias_kind":"arxiv_version","alias_value":"1302.0196v1","created_at":"2026-05-18T03:34:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.0196","created_at":"2026-05-18T03:34:47Z"},{"alias_kind":"pith_short_12","alias_value":"7ZKVA3ZKIL3G","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"7ZKVA3ZKIL3GFCOH","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"7ZKVA3ZK","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:7ZKVA3ZKIL3GFCOH6YL6WFRYRJ","target":"record","payload":{"canonical_record":{"source":{"id":"1302.0196","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-02-01T14:57:40Z","cross_cats_sorted":[],"title_canon_sha256":"8d56e8d6671a55d5a53efc7a65f4ba23e2ea735a51a55cfa38ccbdb8cd5e7eea","abstract_canon_sha256":"a48843632c4fb6b18d73e76b125fcc8c5ef918856ea26c38bb0f269bfaf3b520"},"schema_version":"1.0"},"canonical_sha256":"fe55506f2a42f66289c7f617eb16388a5ecc1fbfe91c2dc61cd358cb895ec3ff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:47.112927Z","signature_b64":"tSjHq7qmXKBuDjEKIwUoApAM2MkPAdMEDs2URtHwyFhSKZdzud1P7URo7JO2nW802BdfNrgGJK1QDyf2b0QCCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe55506f2a42f66289c7f617eb16388a5ecc1fbfe91c2dc61cd358cb895ec3ff","last_reissued_at":"2026-05-18T03:34:47.112086Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:47.112086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.0196","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":"2026-05-18T03:34:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fnAL9p+FWM+wG9MtEB9V+K29m6+/c48p/RCT+r9eoMa7hYLXOlgU8EXu/+LbJHHQ9z4dluRnIX0DcpGwfi1lBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:39:32.015176Z"},"content_sha256":"abccd115ce4ac8edd795b797204d4d75e4cb8893136baa37b4e0b1edb46163b0","schema_version":"1.0","event_id":"sha256:abccd115ce4ac8edd795b797204d4d75e4cb8893136baa37b4e0b1edb46163b0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:7ZKVA3ZKIL3GFCOH6YL6WFRYRJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergence acceleration of Kaczmarz's method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Claude Brezinski, Michela Redivo-Zaglia","submitted_at":"2013-02-01T14:57:40Z","abstract_excerpt":"The method of alternation projections (MAP) is an iterative procedure for finding the projection of a point on the intersection of closed subspaces of an Hilbert space. The convergence of this method is usually slow, and several methods for its acceleration have already been proposed. In this work, we consider a special MAP, namely Kaczmarz' method for solving systems of linear equations. The convergence of this method is discussed. After giving its matrix formulation and its projection properties, we consider several procedures for accelerating its convergence. They are based on sequence tran"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0196","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":"2026-05-18T03:34:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RUZlcDj/yondfrtVQ9wRmDtwfUdPxbQn3DNzI43K/NLJ/Wvah3GRqyBz0WRGjlwZRY3gEDbhi6ziaQzUDnM3Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:39:32.015554Z"},"content_sha256":"5dd21b898791d7f67718ccf671550df61b490663e29acccf6a04901c18930a5e","schema_version":"1.0","event_id":"sha256:5dd21b898791d7f67718ccf671550df61b490663e29acccf6a04901c18930a5e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7ZKVA3ZKIL3GFCOH6YL6WFRYRJ/bundle.json","state_url":"https://pith.science/pith/7ZKVA3ZKIL3GFCOH6YL6WFRYRJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7ZKVA3ZKIL3GFCOH6YL6WFRYRJ/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":"2026-06-05T09:39:32Z","links":{"resolver":"https://pith.science/pith/7ZKVA3ZKIL3GFCOH6YL6WFRYRJ","bundle":"https://pith.science/pith/7ZKVA3ZKIL3GFCOH6YL6WFRYRJ/bundle.json","state":"https://pith.science/pith/7ZKVA3ZKIL3GFCOH6YL6WFRYRJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7ZKVA3ZKIL3GFCOH6YL6WFRYRJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7ZKVA3ZKIL3GFCOH6YL6WFRYRJ","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":"a48843632c4fb6b18d73e76b125fcc8c5ef918856ea26c38bb0f269bfaf3b520","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-02-01T14:57:40Z","title_canon_sha256":"8d56e8d6671a55d5a53efc7a65f4ba23e2ea735a51a55cfa38ccbdb8cd5e7eea"},"schema_version":"1.0","source":{"id":"1302.0196","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.0196","created_at":"2026-05-18T03:34:47Z"},{"alias_kind":"arxiv_version","alias_value":"1302.0196v1","created_at":"2026-05-18T03:34:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.0196","created_at":"2026-05-18T03:34:47Z"},{"alias_kind":"pith_short_12","alias_value":"7ZKVA3ZKIL3G","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"7ZKVA3ZKIL3GFCOH","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"7ZKVA3ZK","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:5dd21b898791d7f67718ccf671550df61b490663e29acccf6a04901c18930a5e","target":"graph","created_at":"2026-05-18T03:34:47Z","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":"The method of alternation projections (MAP) is an iterative procedure for finding the projection of a point on the intersection of closed subspaces of an Hilbert space. The convergence of this method is usually slow, and several methods for its acceleration have already been proposed. In this work, we consider a special MAP, namely Kaczmarz' method for solving systems of linear equations. The convergence of this method is discussed. After giving its matrix formulation and its projection properties, we consider several procedures for accelerating its convergence. They are based on sequence tran","authors_text":"Claude Brezinski, Michela Redivo-Zaglia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-02-01T14:57:40Z","title":"Convergence acceleration of Kaczmarz's method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0196","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:abccd115ce4ac8edd795b797204d4d75e4cb8893136baa37b4e0b1edb46163b0","target":"record","created_at":"2026-05-18T03:34:47Z","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":"a48843632c4fb6b18d73e76b125fcc8c5ef918856ea26c38bb0f269bfaf3b520","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-02-01T14:57:40Z","title_canon_sha256":"8d56e8d6671a55d5a53efc7a65f4ba23e2ea735a51a55cfa38ccbdb8cd5e7eea"},"schema_version":"1.0","source":{"id":"1302.0196","kind":"arxiv","version":1}},"canonical_sha256":"fe55506f2a42f66289c7f617eb16388a5ecc1fbfe91c2dc61cd358cb895ec3ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe55506f2a42f66289c7f617eb16388a5ecc1fbfe91c2dc61cd358cb895ec3ff","first_computed_at":"2026-05-18T03:34:47.112086Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:47.112086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tSjHq7qmXKBuDjEKIwUoApAM2MkPAdMEDs2URtHwyFhSKZdzud1P7URo7JO2nW802BdfNrgGJK1QDyf2b0QCCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:47.112927Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.0196","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:abccd115ce4ac8edd795b797204d4d75e4cb8893136baa37b4e0b1edb46163b0","sha256:5dd21b898791d7f67718ccf671550df61b490663e29acccf6a04901c18930a5e"],"state_sha256":"de207ec602991d6352d06cd17ee6f720f8fd1e36381530298be5797d94e97907"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hGL38wCeURq8N0mYr63KVfqrvFDYRBuJ4YFDpoyCIVnaEasMFP4qaSkfBh5EzdCWsoldW5g8epDIu9ts5UXTDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T09:39:32.017514Z","bundle_sha256":"e4461e381e909a6d2e22f4aa0154441943eb1b6412cb4f278ad23d6f4453fa87"}}