{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:EEAP5ANKOJEGXWUF4ABCQKBUKA","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":"54c97ee04c11cf8f6ad569474a2239102a0aff62074c455bc21c4f107a261850","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2010-02-09T13:55:49Z","title_canon_sha256":"ce32e5e419df50017f3d1a8940168494cf0afb9630eff1e74c37cb88dcef6952"},"schema_version":"1.0","source":{"id":"1002.1859","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.1859","created_at":"2026-05-18T03:55:03Z"},{"alias_kind":"arxiv_version","alias_value":"1002.1859v3","created_at":"2026-05-18T03:55:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.1859","created_at":"2026-05-18T03:55:03Z"},{"alias_kind":"pith_short_12","alias_value":"EEAP5ANKOJEG","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"EEAP5ANKOJEGXWUF","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"EEAP5ANK","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:98e8e9a793ab506b56c8c4971b26aa872b1b9e888f8ee7189151602b8dcccaa8","target":"graph","created_at":"2026-05-18T03:55:03Z","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":"We derive a three-term recurrence relation for computing the polynomial of best approximation in the uniform norm to $x^{-1}$ on a finite interval with positive endpoints. As application, we consider two-level methods for scalar elliptic partial differential equation (PDE), where the relaxation on the fine grid uses the aforementioned polynomial of best approximation. Based on a new smoothing property of this polynomial smoother that we prove, combined with a proper choice of the coarse space, we obtain as a corollary, that the convergence rate of the resulting two-level method is uniform with","authors_text":"Johannes K. Kraus, Ludmil T. Zikatanov, Panayot S. Vassilevski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2010-02-09T13:55:49Z","title":"Polynomial of best uniform approximation to $x^{-1}$ and smoothing in two-level methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.1859","kind":"arxiv","version":3},"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":"sha256:983d2fa5c30e56bd1897f63fac8db5f30d58ba558b62a06f055e53c3e40df284","target":"record","created_at":"2026-05-18T03:55:03Z","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":"54c97ee04c11cf8f6ad569474a2239102a0aff62074c455bc21c4f107a261850","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2010-02-09T13:55:49Z","title_canon_sha256":"ce32e5e419df50017f3d1a8940168494cf0afb9630eff1e74c37cb88dcef6952"},"schema_version":"1.0","source":{"id":"1002.1859","kind":"arxiv","version":3}},"canonical_sha256":"2100fe81aa72486bda85e002282834503860c2d16eeb622810e97d8fbf1f5096","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2100fe81aa72486bda85e002282834503860c2d16eeb622810e97d8fbf1f5096","first_computed_at":"2026-05-18T03:55:03.020460Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:03.020460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7S8Xxe5OWRgTrM5OSmvJrK5Hcf/9AuwXLD+hwoM3DzcYZtv1nqiZ++6bEzaSpq1jkXDc/x3cSH4PVth12cU4Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:03.021194Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.1859","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:983d2fa5c30e56bd1897f63fac8db5f30d58ba558b62a06f055e53c3e40df284","sha256:98e8e9a793ab506b56c8c4971b26aa872b1b9e888f8ee7189151602b8dcccaa8"],"state_sha256":"897bceb93daf0b336d750ec00546c60a8cdf3a9c8bdb6fdc8a6b1046be27c196"}