{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7QCNRMP5ZVK5SQ3K5QUHHUM5HM","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":"e059fbb7cf0a0d7384ffc3e14534b96a043beb25259f0a098e1b98f6598ead14","cross_cats_sorted":["math.CA","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-10-04T18:17:23Z","title_canon_sha256":"d4f836c4ef9ff9c7495ba222c0159a6c826f3642480ec143708c686d58748939"},"schema_version":"1.0","source":{"id":"1310.1356","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.1356","created_at":"2026-05-18T03:11:22Z"},{"alias_kind":"arxiv_version","alias_value":"1310.1356v1","created_at":"2026-05-18T03:11:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.1356","created_at":"2026-05-18T03:11:22Z"},{"alias_kind":"pith_short_12","alias_value":"7QCNRMP5ZVK5","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7QCNRMP5ZVK5SQ3K","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7QCNRMP5","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:fb75c3b5dbd9b9a063fc9640ebf307b1e36a4eaab7a6bb00a410c84e2f3a7fa7","target":"graph","created_at":"2026-05-18T03:11:22Z","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":"It has been recently shown that $|| F_n(A) ||\\leq 2$, where $A$ is a linear continuous operator acting in a Hilbert space, and $F_n$ is the Faber polynomial of degree $n$ corresponding to some convex compact $E\\subset \\mathbb C$ containing the numerical range of $A$. Such an inequality is useful in numerical linear algebra, it allows for instance to derive error bounds for Krylov subspace methods. In the present paper we extend this result to not necessary convex sets $E$.","authors_text":"Bernhard Beckermann (LPP), Michel Crouzeix (IRMAR)","cross_cats":["math.CA","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-10-04T18:17:23Z","title":"Faber polynomials of matrices for non-convex sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1356","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:b5906567f7812eb36a5a3d7a34e26d1d011e215b0ff11f84e042bb2a3c7b7294","target":"record","created_at":"2026-05-18T03:11:22Z","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":"e059fbb7cf0a0d7384ffc3e14534b96a043beb25259f0a098e1b98f6598ead14","cross_cats_sorted":["math.CA","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-10-04T18:17:23Z","title_canon_sha256":"d4f836c4ef9ff9c7495ba222c0159a6c826f3642480ec143708c686d58748939"},"schema_version":"1.0","source":{"id":"1310.1356","kind":"arxiv","version":1}},"canonical_sha256":"fc04d8b1fdcd55d9436aec2873d19d3b14b59e4b7a31cea7ea5f2b7b387c95e8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc04d8b1fdcd55d9436aec2873d19d3b14b59e4b7a31cea7ea5f2b7b387c95e8","first_computed_at":"2026-05-18T03:11:22.550213Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:22.550213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rL3paoku614tE5TVYCZr8RRYSzTa8frvh5ZyOfWK7+vOUHZlqrlPrCF+12Lot4iR79SG75uuz0eVYQ5jwEKNDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:22.550759Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.1356","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5906567f7812eb36a5a3d7a34e26d1d011e215b0ff11f84e042bb2a3c7b7294","sha256:fb75c3b5dbd9b9a063fc9640ebf307b1e36a4eaab7a6bb00a410c84e2f3a7fa7"],"state_sha256":"218131c74e824f346bc5c907d63055a01e9a36399ce5cff33d94eddfcd0fe0cd"}