{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:CGZ5JAI7ZCHA5XLPQSFLNU5DGS","short_pith_number":"pith:CGZ5JAI7","schema_version":"1.0","canonical_sha256":"11b3d4811fc88e0edd6f848ab6d3a334915c5cd69c144cb591d64fa5db04b172","source":{"kind":"arxiv","id":"1807.10715","version":1},"attestation_state":"computed","paper":{"title":"Residual-based iterations for the generalized Lyapunov equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Emil Ringh, Tobias Breiten","submitted_at":"2018-07-27T16:35:21Z","abstract_excerpt":"This paper treats iterative solution methods to the generalized Lyapunov equation. Specifically it expands the existing theoretical justification for the alternating linear scheme (ALS) from the stable Lyapunov equation to the stable generalized Lyapunov equation. Moreover, connections between the energy-norm minimization in ALS and the theory to H2-optimality of an associated bilinear control system are established. It is also shown that a certain ALS-based iteration can be seen as iteratively constructing rank-1 model reduction subspaces for bilinear control systems associated with the resid"},"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":"1807.10715","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-07-27T16:35:21Z","cross_cats_sorted":[],"title_canon_sha256":"26637302fc6841ed8dc5feee06d1e50b4830212596ebbe234d1db9bf9354a0df","abstract_canon_sha256":"3a77b3b96f8590344a9b21a191e5c340b33058e7d5b31e6e1f558747e8e29769"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:17.768014Z","signature_b64":"7RhC/p0IrRQQ7fP2LELxUO9q/ZMShcjOKR+A8jhA0pbQirgEt3zTIaPtaa/FIlUvTWZcfMG9r5lqt7XTJuU2CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"11b3d4811fc88e0edd6f848ab6d3a334915c5cd69c144cb591d64fa5db04b172","last_reissued_at":"2026-05-17T23:43:17.767399Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:17.767399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Residual-based iterations for the generalized Lyapunov equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Emil Ringh, Tobias Breiten","submitted_at":"2018-07-27T16:35:21Z","abstract_excerpt":"This paper treats iterative solution methods to the generalized Lyapunov equation. Specifically it expands the existing theoretical justification for the alternating linear scheme (ALS) from the stable Lyapunov equation to the stable generalized Lyapunov equation. Moreover, connections between the energy-norm minimization in ALS and the theory to H2-optimality of an associated bilinear control system are established. It is also shown that a certain ALS-based iteration can be seen as iteratively constructing rank-1 model reduction subspaces for bilinear control systems associated with the resid"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.10715","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":"1807.10715","created_at":"2026-05-17T23:43:17.767491+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.10715v1","created_at":"2026-05-17T23:43:17.767491+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.10715","created_at":"2026-05-17T23:43:17.767491+00:00"},{"alias_kind":"pith_short_12","alias_value":"CGZ5JAI7ZCHA","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_16","alias_value":"CGZ5JAI7ZCHA5XLP","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_8","alias_value":"CGZ5JAI7","created_at":"2026-05-18T12:32:16.446611+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/CGZ5JAI7ZCHA5XLPQSFLNU5DGS","json":"https://pith.science/pith/CGZ5JAI7ZCHA5XLPQSFLNU5DGS.json","graph_json":"https://pith.science/api/pith-number/CGZ5JAI7ZCHA5XLPQSFLNU5DGS/graph.json","events_json":"https://pith.science/api/pith-number/CGZ5JAI7ZCHA5XLPQSFLNU5DGS/events.json","paper":"https://pith.science/paper/CGZ5JAI7"},"agent_actions":{"view_html":"https://pith.science/pith/CGZ5JAI7ZCHA5XLPQSFLNU5DGS","download_json":"https://pith.science/pith/CGZ5JAI7ZCHA5XLPQSFLNU5DGS.json","view_paper":"https://pith.science/paper/CGZ5JAI7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.10715&json=true","fetch_graph":"https://pith.science/api/pith-number/CGZ5JAI7ZCHA5XLPQSFLNU5DGS/graph.json","fetch_events":"https://pith.science/api/pith-number/CGZ5JAI7ZCHA5XLPQSFLNU5DGS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CGZ5JAI7ZCHA5XLPQSFLNU5DGS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CGZ5JAI7ZCHA5XLPQSFLNU5DGS/action/storage_attestation","attest_author":"https://pith.science/pith/CGZ5JAI7ZCHA5XLPQSFLNU5DGS/action/author_attestation","sign_citation":"https://pith.science/pith/CGZ5JAI7ZCHA5XLPQSFLNU5DGS/action/citation_signature","submit_replication":"https://pith.science/pith/CGZ5JAI7ZCHA5XLPQSFLNU5DGS/action/replication_record"}},"created_at":"2026-05-17T23:43:17.767491+00:00","updated_at":"2026-05-17T23:43:17.767491+00:00"}