{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:GMMAATUG7F6CQ7PM242NJVE7GX","short_pith_number":"pith:GMMAATUG","schema_version":"1.0","canonical_sha256":"3318004e86f97c287decd734d4d49f35ffb2389a4b12c663643deb73f9099486","source":{"kind":"arxiv","id":"1510.01073","version":2},"attestation_state":"computed","paper":{"title":"On the correction equation of the Jacobi-Davidson method","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Gang Wu, Hong-kui Pang","submitted_at":"2015-10-05T09:25:42Z","abstract_excerpt":"The Jacobi-Davidson method is one of the most popular approaches for iteratively computing a few eigenvalues and their associated eigenvectors of a large matrix. The key of this method is to expand the search subspace via solving the Jacobi-Davidson correction equation, whose coefficient matrix is singular. It is believed long by scholars that the Jacobi-Davidson correction equation is a consistent linear system. In this work, we point out that the correction equation may have a unique solution or have no solution at all, and we derive a computable necessary and sufficient condition for cheapl"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1510.01073","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NA","submitted_at":"2015-10-05T09:25:42Z","cross_cats_sorted":[],"title_canon_sha256":"91001a0a5ddce603358d16504810b7686e80dcf279c98c4311f5f4107db12a96","abstract_canon_sha256":"406a7cb8aaea9b53c2926b5471286d9db6cfd8244d4aa821f17848387d23b31c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:56.715780Z","signature_b64":"8+Wv/aTVvFCKRmpm36OZQjl2kR4QANnU4Wg9Uy4aQpfTAe2DjlvrH0/RzlIdkecIAUkL+wmfRBhH4a7P8oE+Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3318004e86f97c287decd734d4d49f35ffb2389a4b12c663643deb73f9099486","last_reissued_at":"2026-05-18T01:27:56.715086Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:56.715086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the correction equation of the Jacobi-Davidson method","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Gang Wu, Hong-kui Pang","submitted_at":"2015-10-05T09:25:42Z","abstract_excerpt":"The Jacobi-Davidson method is one of the most popular approaches for iteratively computing a few eigenvalues and their associated eigenvectors of a large matrix. The key of this method is to expand the search subspace via solving the Jacobi-Davidson correction equation, whose coefficient matrix is singular. It is believed long by scholars that the Jacobi-Davidson correction equation is a consistent linear system. In this work, we point out that the correction equation may have a unique solution or have no solution at all, and we derive a computable necessary and sufficient condition for cheapl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01073","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1510.01073","created_at":"2026-05-18T01:27:56.715189+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.01073v2","created_at":"2026-05-18T01:27:56.715189+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.01073","created_at":"2026-05-18T01:27:56.715189+00:00"},{"alias_kind":"pith_short_12","alias_value":"GMMAATUG7F6C","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"GMMAATUG7F6CQ7PM","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"GMMAATUG","created_at":"2026-05-18T12:29:22.688609+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GMMAATUG7F6CQ7PM242NJVE7GX","json":"https://pith.science/pith/GMMAATUG7F6CQ7PM242NJVE7GX.json","graph_json":"https://pith.science/api/pith-number/GMMAATUG7F6CQ7PM242NJVE7GX/graph.json","events_json":"https://pith.science/api/pith-number/GMMAATUG7F6CQ7PM242NJVE7GX/events.json","paper":"https://pith.science/paper/GMMAATUG"},"agent_actions":{"view_html":"https://pith.science/pith/GMMAATUG7F6CQ7PM242NJVE7GX","download_json":"https://pith.science/pith/GMMAATUG7F6CQ7PM242NJVE7GX.json","view_paper":"https://pith.science/paper/GMMAATUG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.01073&json=true","fetch_graph":"https://pith.science/api/pith-number/GMMAATUG7F6CQ7PM242NJVE7GX/graph.json","fetch_events":"https://pith.science/api/pith-number/GMMAATUG7F6CQ7PM242NJVE7GX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GMMAATUG7F6CQ7PM242NJVE7GX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GMMAATUG7F6CQ7PM242NJVE7GX/action/storage_attestation","attest_author":"https://pith.science/pith/GMMAATUG7F6CQ7PM242NJVE7GX/action/author_attestation","sign_citation":"https://pith.science/pith/GMMAATUG7F6CQ7PM242NJVE7GX/action/citation_signature","submit_replication":"https://pith.science/pith/GMMAATUG7F6CQ7PM242NJVE7GX/action/replication_record"}},"created_at":"2026-05-18T01:27:56.715189+00:00","updated_at":"2026-05-18T01:27:56.715189+00:00"}