{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:SR2JBNZJQG3FCZVVNM7NNPHSNY","short_pith_number":"pith:SR2JBNZJ","canonical_record":{"source":{"id":"1504.02197","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-04-09T06:20:04Z","cross_cats_sorted":[],"title_canon_sha256":"be62508a15f28209ec8a69f93e99970e2b85fc70b4a1285e399f24aca3ee609a","abstract_canon_sha256":"a0c41f6ccc6bc1e74b2836e7fbf7d9f7e26b4bbfbe33d98dac39acdf75b5edf1"},"schema_version":"1.0"},"canonical_sha256":"947490b72981b65166b56b3ed6bcf26e2281014a450e00dd6591713cc9db415b","source":{"kind":"arxiv","id":"1504.02197","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.02197","created_at":"2026-05-18T02:03:54Z"},{"alias_kind":"arxiv_version","alias_value":"1504.02197v2","created_at":"2026-05-18T02:03:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.02197","created_at":"2026-05-18T02:03:54Z"},{"alias_kind":"pith_short_12","alias_value":"SR2JBNZJQG3F","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SR2JBNZJQG3FCZVV","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SR2JBNZJ","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:SR2JBNZJQG3FCZVVNM7NNPHSNY","target":"record","payload":{"canonical_record":{"source":{"id":"1504.02197","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-04-09T06:20:04Z","cross_cats_sorted":[],"title_canon_sha256":"be62508a15f28209ec8a69f93e99970e2b85fc70b4a1285e399f24aca3ee609a","abstract_canon_sha256":"a0c41f6ccc6bc1e74b2836e7fbf7d9f7e26b4bbfbe33d98dac39acdf75b5edf1"},"schema_version":"1.0"},"canonical_sha256":"947490b72981b65166b56b3ed6bcf26e2281014a450e00dd6591713cc9db415b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:54.653023Z","signature_b64":"qhfX6W6UsnF+gyWSYURiDeNLqnHHoreQ3nJyTr25/K7rg1DW9y7fJgE/LQqbYPGbkFoOWBWhMiJZWu92VUtZAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"947490b72981b65166b56b3ed6bcf26e2281014a450e00dd6591713cc9db415b","last_reissued_at":"2026-05-18T02:03:54.652326Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:54.652326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.02197","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":"2026-05-18T02:03:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S+tgCNzjJR2UMMS++xtJmXxbhoHQs3ZCdxt3A6tc/tQufCKjRJFcL88lDSabmFPugRDxgeCqPQeYK3WdQP0eCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:07:03.825961Z"},"content_sha256":"eb77c62cdcdc0d7a8ec7438d67a61ebde4577f41e1bcfb42666953146c6056cd","schema_version":"1.0","event_id":"sha256:eb77c62cdcdc0d7a8ec7438d67a61ebde4577f41e1bcfb42666953146c6056cd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:SR2JBNZJQG3FCZVVNM7NNPHSNY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An inexact Noda iteration for computing the smallest eigenpair of a large irreducible monotone matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Ching-Sung Liu","submitted_at":"2015-04-09T06:20:04Z","abstract_excerpt":"In this paper, we present an inexact Noda iteration with inner-outer iterations for finding the smallest eigenvalue and the associated eigenvector of an irreducible monotone matrix. The proposed inexact Noda iteration contains two main relaxation steps for computing the smallest eigenvalue and the associated eigenvector, respectively. These relaxation steps depend on the relaxation factors, and we analyze how the relaxation factors in the relaxation steps affect the convergence of the outer iterations. By considering two different relaxation factors for solving the inner linear systems involve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02197","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":""},"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":"2026-05-18T02:03:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X5ddFCEe4unN+qjjKuPzfNBtoyjkRkIomz5hyCJj13hMyPe7XY3b18COhdYkc2XfzCyi8/i47rzdukKMjK4jDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:07:03.826516Z"},"content_sha256":"a3ebe61eac05e8a5ad3ee9bc5afc17f52d6b67bb5dac2a553c8c250bf596a8f8","schema_version":"1.0","event_id":"sha256:a3ebe61eac05e8a5ad3ee9bc5afc17f52d6b67bb5dac2a553c8c250bf596a8f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SR2JBNZJQG3FCZVVNM7NNPHSNY/bundle.json","state_url":"https://pith.science/pith/SR2JBNZJQG3FCZVVNM7NNPHSNY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SR2JBNZJQG3FCZVVNM7NNPHSNY/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":"2026-05-27T18:07:03Z","links":{"resolver":"https://pith.science/pith/SR2JBNZJQG3FCZVVNM7NNPHSNY","bundle":"https://pith.science/pith/SR2JBNZJQG3FCZVVNM7NNPHSNY/bundle.json","state":"https://pith.science/pith/SR2JBNZJQG3FCZVVNM7NNPHSNY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SR2JBNZJQG3FCZVVNM7NNPHSNY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SR2JBNZJQG3FCZVVNM7NNPHSNY","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":"a0c41f6ccc6bc1e74b2836e7fbf7d9f7e26b4bbfbe33d98dac39acdf75b5edf1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-04-09T06:20:04Z","title_canon_sha256":"be62508a15f28209ec8a69f93e99970e2b85fc70b4a1285e399f24aca3ee609a"},"schema_version":"1.0","source":{"id":"1504.02197","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.02197","created_at":"2026-05-18T02:03:54Z"},{"alias_kind":"arxiv_version","alias_value":"1504.02197v2","created_at":"2026-05-18T02:03:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.02197","created_at":"2026-05-18T02:03:54Z"},{"alias_kind":"pith_short_12","alias_value":"SR2JBNZJQG3F","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SR2JBNZJQG3FCZVV","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SR2JBNZJ","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:a3ebe61eac05e8a5ad3ee9bc5afc17f52d6b67bb5dac2a553c8c250bf596a8f8","target":"graph","created_at":"2026-05-18T02:03:54Z","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 present an inexact Noda iteration with inner-outer iterations for finding the smallest eigenvalue and the associated eigenvector of an irreducible monotone matrix. The proposed inexact Noda iteration contains two main relaxation steps for computing the smallest eigenvalue and the associated eigenvector, respectively. These relaxation steps depend on the relaxation factors, and we analyze how the relaxation factors in the relaxation steps affect the convergence of the outer iterations. By considering two different relaxation factors for solving the inner linear systems involve","authors_text":"Ching-Sung Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-04-09T06:20:04Z","title":"An inexact Noda iteration for computing the smallest eigenpair of a large irreducible monotone matrix"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02197","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:eb77c62cdcdc0d7a8ec7438d67a61ebde4577f41e1bcfb42666953146c6056cd","target":"record","created_at":"2026-05-18T02:03:54Z","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":"a0c41f6ccc6bc1e74b2836e7fbf7d9f7e26b4bbfbe33d98dac39acdf75b5edf1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-04-09T06:20:04Z","title_canon_sha256":"be62508a15f28209ec8a69f93e99970e2b85fc70b4a1285e399f24aca3ee609a"},"schema_version":"1.0","source":{"id":"1504.02197","kind":"arxiv","version":2}},"canonical_sha256":"947490b72981b65166b56b3ed6bcf26e2281014a450e00dd6591713cc9db415b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"947490b72981b65166b56b3ed6bcf26e2281014a450e00dd6591713cc9db415b","first_computed_at":"2026-05-18T02:03:54.652326Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:54.652326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qhfX6W6UsnF+gyWSYURiDeNLqnHHoreQ3nJyTr25/K7rg1DW9y7fJgE/LQqbYPGbkFoOWBWhMiJZWu92VUtZAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:54.653023Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.02197","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb77c62cdcdc0d7a8ec7438d67a61ebde4577f41e1bcfb42666953146c6056cd","sha256:a3ebe61eac05e8a5ad3ee9bc5afc17f52d6b67bb5dac2a553c8c250bf596a8f8"],"state_sha256":"82cc6e074b1c1efe6d8e45a908dc41a73cb7470ea727d31ad6dd0e20ddcc2507"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BfshkotqfIdsX5wFrcvDZZ6gj/qR58PpzAPsg/tIJmFbP/6rZabMYu4MVnjGM66z0QF1OEROvrNSNZnhvS3ABQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T18:07:03.829759Z","bundle_sha256":"3c626c736854cfbe3027ba48f6a909e7370ca2f19850773bae31300433dfeb40"}}