{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:3WHE2GZBMOSWPCX3IUYCJM2UQM","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":"ad62f74b401e97589fd5b4013caf533c3e855569b6a9c6ebef20e1245f8e5ab0","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-08-16T22:15:55Z","title_canon_sha256":"8e8a351e75abb4f5202921a18034d63a3933e71890d594f47717c43575f3eb58"},"schema_version":"1.0","source":{"id":"1108.3367","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.3367","created_at":"2026-05-18T04:00:52Z"},{"alias_kind":"arxiv_version","alias_value":"1108.3367v2","created_at":"2026-05-18T04:00:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.3367","created_at":"2026-05-18T04:00:52Z"},{"alias_kind":"pith_short_12","alias_value":"3WHE2GZBMOSW","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"3WHE2GZBMOSWPCX3","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"3WHE2GZB","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:43bb45d1cf91b82ef6123db6efc46b3918867c69c0f8009036e1e01633002dae","target":"graph","created_at":"2026-05-18T04:00:52Z","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":"A well known method for convergence acceleration of continued fraction $\\K(a_n/b_n)$ is to use the modified approximants $S_n(\\omega_n)$ in place of the classical approximants $S_n(0)$, where $\\omega_n$ are close to tails $f^{(n)}$ of continued fraction. Recently, author proposed a method of iterative character producing tail approximations whose asymptotic expansion's accuracy is improving in each step. This method can be applied to continued fractions $\\K(a_n/b_n)$, where $a_n$, $b_n$ are polynomials in $n$ ($\\deg a_n=2$, $\\deg b_n\\leq 1$) for sufficiently large $n$. The purpose of this pape","authors_text":"Rafa{\\l} Nowak","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-08-16T22:15:55Z","title":"On the convergence acceleration of some continued fractions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3367","kind":"arxiv","version":2},"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:ac6e26f4066059867229cbd2b8f5f186881f63df29891d586e306ee7ac7b9372","target":"record","created_at":"2026-05-18T04:00:52Z","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":"ad62f74b401e97589fd5b4013caf533c3e855569b6a9c6ebef20e1245f8e5ab0","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-08-16T22:15:55Z","title_canon_sha256":"8e8a351e75abb4f5202921a18034d63a3933e71890d594f47717c43575f3eb58"},"schema_version":"1.0","source":{"id":"1108.3367","kind":"arxiv","version":2}},"canonical_sha256":"dd8e4d1b2163a5678afb453024b3548313886823b6ed5ae1c4883d8167f63d02","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd8e4d1b2163a5678afb453024b3548313886823b6ed5ae1c4883d8167f63d02","first_computed_at":"2026-05-18T04:00:52.108491Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:00:52.108491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xeehJ5HVdUsN0II0SaTa+qMijzdMGrhj6JTwhf+fEvJzEhnTwvNVdCn3FN9XPHYSy3tzTEsaQayky1pn3KLcDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:00:52.109446Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.3367","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac6e26f4066059867229cbd2b8f5f186881f63df29891d586e306ee7ac7b9372","sha256:43bb45d1cf91b82ef6123db6efc46b3918867c69c0f8009036e1e01633002dae"],"state_sha256":"5eb08199802e3c12e0f4300f121400c5274342ae8759565ba3679095bfe56402"}