{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:L55ZXH4KQEWHLKZ3CXVSQHC3EQ","short_pith_number":"pith:L55ZXH4K","schema_version":"1.0","canonical_sha256":"5f7b9b9f8a812c75ab3b15eb281c5b24383b9d7ffa1c4dbcae949b0edc8e90e2","source":{"kind":"arxiv","id":"2502.09165","version":4},"attestation_state":"computed","paper":{"title":"Generalizing Reduced Rank Extrapolation to Low-Rank Matrix Sequences","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Jens Saak, Jonas Schulze, Jos Maubach, Nathan van de Wouw, Pascal den Boef, Patrick K\\\"urschner, Wil Schilders, Xiaobo Liu","submitted_at":"2025-02-13T10:48:46Z","abstract_excerpt":"Reduced rank extrapolation (RRE) is an acceleration method typically used to accelerate the iterative solution of nonlinear systems of equations using a fixed-point process. In this context, the iterates are vectors generated from a fixed-point mapping function. However, when considering the iterative solution of large-scale matrix equations, the iterates are low-rank matrices generated from a fixed-point process for which, generally, the mapping function changes in each iteration. To enable acceleration of the iterative solution for these problems, we propose two novel generalizations of RRE."},"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":"2502.09165","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-02-13T10:48:46Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"992e807da36699d1225b4cba714600e7ab9433ec31e98ba3af2c47c7ee2f699b","abstract_canon_sha256":"c111748c95eefe68285b5967bc58b07b132b2c54a4b4e2efc1a64813a8294db8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-22T01:04:53.359659Z","signature_b64":"1hxgN7FECEY1KmWEC54yrOyOeblxw1JwP6wFGk7ZpGI1E3nvZZFN5p4DdxCYHe45J4Ht8TMWLFYn48cs5KmNAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f7b9b9f8a812c75ab3b15eb281c5b24383b9d7ffa1c4dbcae949b0edc8e90e2","last_reissued_at":"2026-05-22T01:04:53.358952Z","signature_status":"signed_v1","first_computed_at":"2026-05-22T01:04:53.358952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalizing Reduced Rank Extrapolation to Low-Rank Matrix Sequences","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Jens Saak, Jonas Schulze, Jos Maubach, Nathan van de Wouw, Pascal den Boef, Patrick K\\\"urschner, Wil Schilders, Xiaobo Liu","submitted_at":"2025-02-13T10:48:46Z","abstract_excerpt":"Reduced rank extrapolation (RRE) is an acceleration method typically used to accelerate the iterative solution of nonlinear systems of equations using a fixed-point process. In this context, the iterates are vectors generated from a fixed-point mapping function. However, when considering the iterative solution of large-scale matrix equations, the iterates are low-rank matrices generated from a fixed-point process for which, generally, the mapping function changes in each iteration. To enable acceleration of the iterative solution for these problems, we propose two novel generalizations of RRE."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.09165","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.09165/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2502.09165","created_at":"2026-05-22T01:04:53.359051+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.09165v4","created_at":"2026-05-22T01:04:53.359051+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.09165","created_at":"2026-05-22T01:04:53.359051+00:00"},{"alias_kind":"pith_short_12","alias_value":"L55ZXH4KQEWH","created_at":"2026-05-22T01:04:53.359051+00:00"},{"alias_kind":"pith_short_16","alias_value":"L55ZXH4KQEWHLKZ3","created_at":"2026-05-22T01:04:53.359051+00:00"},{"alias_kind":"pith_short_8","alias_value":"L55ZXH4K","created_at":"2026-05-22T01:04:53.359051+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/L55ZXH4KQEWHLKZ3CXVSQHC3EQ","json":"https://pith.science/pith/L55ZXH4KQEWHLKZ3CXVSQHC3EQ.json","graph_json":"https://pith.science/api/pith-number/L55ZXH4KQEWHLKZ3CXVSQHC3EQ/graph.json","events_json":"https://pith.science/api/pith-number/L55ZXH4KQEWHLKZ3CXVSQHC3EQ/events.json","paper":"https://pith.science/paper/L55ZXH4K"},"agent_actions":{"view_html":"https://pith.science/pith/L55ZXH4KQEWHLKZ3CXVSQHC3EQ","download_json":"https://pith.science/pith/L55ZXH4KQEWHLKZ3CXVSQHC3EQ.json","view_paper":"https://pith.science/paper/L55ZXH4K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.09165&json=true","fetch_graph":"https://pith.science/api/pith-number/L55ZXH4KQEWHLKZ3CXVSQHC3EQ/graph.json","fetch_events":"https://pith.science/api/pith-number/L55ZXH4KQEWHLKZ3CXVSQHC3EQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L55ZXH4KQEWHLKZ3CXVSQHC3EQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L55ZXH4KQEWHLKZ3CXVSQHC3EQ/action/storage_attestation","attest_author":"https://pith.science/pith/L55ZXH4KQEWHLKZ3CXVSQHC3EQ/action/author_attestation","sign_citation":"https://pith.science/pith/L55ZXH4KQEWHLKZ3CXVSQHC3EQ/action/citation_signature","submit_replication":"https://pith.science/pith/L55ZXH4KQEWHLKZ3CXVSQHC3EQ/action/replication_record"}},"created_at":"2026-05-22T01:04:53.359051+00:00","updated_at":"2026-05-22T01:04:53.359051+00:00"}