{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:YV7JDWTYWHOBUEZKITLAS32H3R","short_pith_number":"pith:YV7JDWTY","schema_version":"1.0","canonical_sha256":"c57e91da78b1dc1a132a44d6096f47dc50a9a55a904c5199ffb4387317e152b1","source":{"kind":"arxiv","id":"1701.04157","version":1},"attestation_state":"computed","paper":{"title":"A modified generalized shift-splitting preconditioner for nonsymmetric saddle point problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Jingjing Cui, Ligong Wang, Zhengge Huang, Zhong Xu","submitted_at":"2017-01-16T03:48:03Z","abstract_excerpt":"For the nonsymmetric saddle point problems with nonsymmetric positive definite (1,1) parts, the modified generalized shift-splitting (MGSSP) preconditioner as well as the MGSSP iteration method are derived in this paper, which generalize the MSSP preconditioner and the MSSP iteration method newly developed by Huang and Su (J. Comput. Appl. Math. 2017), respectively. The convergent and semi-convergent analysis of the MGSSP iteration method are presented, and we prove that this method is unconditionally convergent and semi-convergent. In addition, some spectral properties of the preconditioned m"},"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":"1701.04157","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-01-16T03:48:03Z","cross_cats_sorted":[],"title_canon_sha256":"4bf8c474da89922ae887c1c75d840bd5d962cab135010b94be6c271e43739dbe","abstract_canon_sha256":"d7d95e16e154b41cf3e9a5bf8f2e898c1b046e9e6260c785f1aa8b94416c36cd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:47.673481Z","signature_b64":"1CfHbEhvpvMXr0+eiU3Ml7DLMMyFfcE6rwZavcPml78yQbFtbdNlp4d3xvN/2s5jLqF272eCxyycCEc0NPSDDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c57e91da78b1dc1a132a44d6096f47dc50a9a55a904c5199ffb4387317e152b1","last_reissued_at":"2026-05-18T00:52:47.672844Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:47.672844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A modified generalized shift-splitting preconditioner for nonsymmetric saddle point problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Jingjing Cui, Ligong Wang, Zhengge Huang, Zhong Xu","submitted_at":"2017-01-16T03:48:03Z","abstract_excerpt":"For the nonsymmetric saddle point problems with nonsymmetric positive definite (1,1) parts, the modified generalized shift-splitting (MGSSP) preconditioner as well as the MGSSP iteration method are derived in this paper, which generalize the MSSP preconditioner and the MSSP iteration method newly developed by Huang and Su (J. Comput. Appl. Math. 2017), respectively. The convergent and semi-convergent analysis of the MGSSP iteration method are presented, and we prove that this method is unconditionally convergent and semi-convergent. In addition, some spectral properties of the preconditioned m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04157","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1701.04157","created_at":"2026-05-18T00:52:47.672926+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.04157v1","created_at":"2026-05-18T00:52:47.672926+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.04157","created_at":"2026-05-18T00:52:47.672926+00:00"},{"alias_kind":"pith_short_12","alias_value":"YV7JDWTYWHOB","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_16","alias_value":"YV7JDWTYWHOBUEZK","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_8","alias_value":"YV7JDWTY","created_at":"2026-05-18T12:31:56.362134+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/YV7JDWTYWHOBUEZKITLAS32H3R","json":"https://pith.science/pith/YV7JDWTYWHOBUEZKITLAS32H3R.json","graph_json":"https://pith.science/api/pith-number/YV7JDWTYWHOBUEZKITLAS32H3R/graph.json","events_json":"https://pith.science/api/pith-number/YV7JDWTYWHOBUEZKITLAS32H3R/events.json","paper":"https://pith.science/paper/YV7JDWTY"},"agent_actions":{"view_html":"https://pith.science/pith/YV7JDWTYWHOBUEZKITLAS32H3R","download_json":"https://pith.science/pith/YV7JDWTYWHOBUEZKITLAS32H3R.json","view_paper":"https://pith.science/paper/YV7JDWTY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.04157&json=true","fetch_graph":"https://pith.science/api/pith-number/YV7JDWTYWHOBUEZKITLAS32H3R/graph.json","fetch_events":"https://pith.science/api/pith-number/YV7JDWTYWHOBUEZKITLAS32H3R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YV7JDWTYWHOBUEZKITLAS32H3R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YV7JDWTYWHOBUEZKITLAS32H3R/action/storage_attestation","attest_author":"https://pith.science/pith/YV7JDWTYWHOBUEZKITLAS32H3R/action/author_attestation","sign_citation":"https://pith.science/pith/YV7JDWTYWHOBUEZKITLAS32H3R/action/citation_signature","submit_replication":"https://pith.science/pith/YV7JDWTYWHOBUEZKITLAS32H3R/action/replication_record"}},"created_at":"2026-05-18T00:52:47.672926+00:00","updated_at":"2026-05-18T00:52:47.672926+00:00"}