{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ITU3PIYLEC7QBD2TUFNNOXUU3L","short_pith_number":"pith:ITU3PIYL","canonical_record":{"source":{"id":"1506.06829","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-06-23T00:08:39Z","cross_cats_sorted":[],"title_canon_sha256":"3fc0ab82c90508bf343ddae85a1fda7c93252f3e7d9e324012cb358b8d48a51a","abstract_canon_sha256":"d1df9b3315453736005dfc8a4beac54bf991cf3697effdff75860a7de816daa2"},"schema_version":"1.0"},"canonical_sha256":"44e9b7a30b20bf008f53a15ad75e94dac713496628a0cd9b770a758b84148c4b","source":{"kind":"arxiv","id":"1506.06829","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.06829","created_at":"2026-05-18T01:40:55Z"},{"alias_kind":"arxiv_version","alias_value":"1506.06829v1","created_at":"2026-05-18T01:40:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06829","created_at":"2026-05-18T01:40:55Z"},{"alias_kind":"pith_short_12","alias_value":"ITU3PIYLEC7Q","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"ITU3PIYLEC7QBD2T","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"ITU3PIYL","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ITU3PIYLEC7QBD2TUFNNOXUU3L","target":"record","payload":{"canonical_record":{"source":{"id":"1506.06829","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-06-23T00:08:39Z","cross_cats_sorted":[],"title_canon_sha256":"3fc0ab82c90508bf343ddae85a1fda7c93252f3e7d9e324012cb358b8d48a51a","abstract_canon_sha256":"d1df9b3315453736005dfc8a4beac54bf991cf3697effdff75860a7de816daa2"},"schema_version":"1.0"},"canonical_sha256":"44e9b7a30b20bf008f53a15ad75e94dac713496628a0cd9b770a758b84148c4b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:40:55.869933Z","signature_b64":"/dOr9ZN5ac1QeEQLgUCcB39sZOfZTKzCa6gOKL4/OkpDaN9Sciz/leZJUI3PAQ/jTPmsaLBFdfLJ6MzyNVK9AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"44e9b7a30b20bf008f53a15ad75e94dac713496628a0cd9b770a758b84148c4b","last_reissued_at":"2026-05-18T01:40:55.869189Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:40:55.869189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.06829","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":"2026-05-18T01:40:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"elmfDM68uDOT4f/+VEcpKWRcXjYNEo4Knw5JwDQ59N+A5mIq9qnehT4edpF5kHCMIop3LWb7HVRkvryryis4BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T11:35:02.687453Z"},"content_sha256":"a8e9a983c442927ad54d7abaef6579dab97ede41ab84035105ab1399032ea41a","schema_version":"1.0","event_id":"sha256:a8e9a983c442927ad54d7abaef6579dab97ede41ab84035105ab1399032ea41a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ITU3PIYLEC7QBD2TUFNNOXUU3L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized preconditioned locally harmonic residual method for non-Hermitian eigenproblems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Chao Yang, Eugene Vecharynski, Fei Xue","submitted_at":"2015-06-23T00:08:39Z","abstract_excerpt":"We introduce the Generalized Preconditioned Locally Harmonic Residual (GPLHR) method for solving standard and generalized non-Hermitian eigenproblems. The method is particularly useful for computing a subset of eigenvalues, and their eigen- or Schur vectors, closest to a given shift. The proposed method is based on block iterations and can take advantage of a preconditioner if it is available. It does not need to perform exact shift-and-invert transformation. Standard and generalized eigenproblems are handled in a unified framework. Our numerical experiments demonstrate that GPLHR is generally"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06829","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":"2026-05-18T01:40:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5ju796iI10Y9t3W7thoTFNuJhVWJldxFeAtiAbU/6l+Ai5xU/5MlUaHxGfZjfsFy6VlZKFAVserE0rxYmDnoBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T11:35:02.687797Z"},"content_sha256":"d2eb9d8d2a23251ae2d986b37a98fdf6acc4e96bdbd64b39715ba6701779bfd0","schema_version":"1.0","event_id":"sha256:d2eb9d8d2a23251ae2d986b37a98fdf6acc4e96bdbd64b39715ba6701779bfd0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ITU3PIYLEC7QBD2TUFNNOXUU3L/bundle.json","state_url":"https://pith.science/pith/ITU3PIYLEC7QBD2TUFNNOXUU3L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ITU3PIYLEC7QBD2TUFNNOXUU3L/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":"2026-05-28T11:35:02Z","links":{"resolver":"https://pith.science/pith/ITU3PIYLEC7QBD2TUFNNOXUU3L","bundle":"https://pith.science/pith/ITU3PIYLEC7QBD2TUFNNOXUU3L/bundle.json","state":"https://pith.science/pith/ITU3PIYLEC7QBD2TUFNNOXUU3L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ITU3PIYLEC7QBD2TUFNNOXUU3L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ITU3PIYLEC7QBD2TUFNNOXUU3L","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":"d1df9b3315453736005dfc8a4beac54bf991cf3697effdff75860a7de816daa2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-06-23T00:08:39Z","title_canon_sha256":"3fc0ab82c90508bf343ddae85a1fda7c93252f3e7d9e324012cb358b8d48a51a"},"schema_version":"1.0","source":{"id":"1506.06829","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.06829","created_at":"2026-05-18T01:40:55Z"},{"alias_kind":"arxiv_version","alias_value":"1506.06829v1","created_at":"2026-05-18T01:40:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06829","created_at":"2026-05-18T01:40:55Z"},{"alias_kind":"pith_short_12","alias_value":"ITU3PIYLEC7Q","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"ITU3PIYLEC7QBD2T","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"ITU3PIYL","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:d2eb9d8d2a23251ae2d986b37a98fdf6acc4e96bdbd64b39715ba6701779bfd0","target":"graph","created_at":"2026-05-18T01:40:55Z","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":"We introduce the Generalized Preconditioned Locally Harmonic Residual (GPLHR) method for solving standard and generalized non-Hermitian eigenproblems. The method is particularly useful for computing a subset of eigenvalues, and their eigen- or Schur vectors, closest to a given shift. The proposed method is based on block iterations and can take advantage of a preconditioner if it is available. It does not need to perform exact shift-and-invert transformation. Standard and generalized eigenproblems are handled in a unified framework. Our numerical experiments demonstrate that GPLHR is generally","authors_text":"Chao Yang, Eugene Vecharynski, Fei Xue","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-06-23T00:08:39Z","title":"Generalized preconditioned locally harmonic residual method for non-Hermitian eigenproblems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06829","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:a8e9a983c442927ad54d7abaef6579dab97ede41ab84035105ab1399032ea41a","target":"record","created_at":"2026-05-18T01:40:55Z","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":"d1df9b3315453736005dfc8a4beac54bf991cf3697effdff75860a7de816daa2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-06-23T00:08:39Z","title_canon_sha256":"3fc0ab82c90508bf343ddae85a1fda7c93252f3e7d9e324012cb358b8d48a51a"},"schema_version":"1.0","source":{"id":"1506.06829","kind":"arxiv","version":1}},"canonical_sha256":"44e9b7a30b20bf008f53a15ad75e94dac713496628a0cd9b770a758b84148c4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"44e9b7a30b20bf008f53a15ad75e94dac713496628a0cd9b770a758b84148c4b","first_computed_at":"2026-05-18T01:40:55.869189Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:40:55.869189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/dOr9ZN5ac1QeEQLgUCcB39sZOfZTKzCa6gOKL4/OkpDaN9Sciz/leZJUI3PAQ/jTPmsaLBFdfLJ6MzyNVK9AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:40:55.869933Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.06829","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a8e9a983c442927ad54d7abaef6579dab97ede41ab84035105ab1399032ea41a","sha256:d2eb9d8d2a23251ae2d986b37a98fdf6acc4e96bdbd64b39715ba6701779bfd0"],"state_sha256":"087747951fddf75f0e8c9e718ddc92d7f821a46b1578033279cd85849f30dd84"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G477grNxM8RfLoKPm1JuMuFrmed0MItD7nQHkw0pf+7Tlh+EN4nOORirW96zL1OUrNsYrtqzglhGQiI6VsjxCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T11:35:02.689711Z","bundle_sha256":"002815ac1c79c93525316d1b48171c299fd51fe434ba68ceedb43d6fbc96db0e"}}