{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6VBDODCFUHFFANKNWA22JTKVQD","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":"e0bdbc43458c0e10ec4e5a83d6efb530ded7021947844c1af55267f00aa64453","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-10-23T04:38:27Z","title_canon_sha256":"0f7371f517629c773037978b7382b791d323114101fc202c18e51804e5bd1c44"},"schema_version":"1.0","source":{"id":"1510.06823","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.06823","created_at":"2026-05-18T00:08:05Z"},{"alias_kind":"arxiv_version","alias_value":"1510.06823v3","created_at":"2026-05-18T00:08:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.06823","created_at":"2026-05-18T00:08:05Z"},{"alias_kind":"pith_short_12","alias_value":"6VBDODCFUHFF","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6VBDODCFUHFFANKN","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6VBDODCF","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:04659be3aff52c6550f48a0f1e225a61fa20ba4f1e4561592f23aaf36e0c5da1","target":"graph","created_at":"2026-05-18T00:08:05Z","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":"In this paper, we establish sublinear and linear convergence of fixed point iterations generated by averaged operators in a Hilbert space. Our results are achieved under a bounded H\\\"older regularity assumption which generalizes the well-known notion of bounded linear regularity. As an application of our results, we provide a convergence rate analysis for Krasnoselskii-Mann iterations, the cyclic projection algorithm, and the Douglas-Rachford feasibility algorithm along with some variants. In the important case in which the underlying sets are convex sets described by convex polynomials in a f","authors_text":"Guoyin Li, Jonathan M. Borwein, Matthew K. Tam","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-10-23T04:38:27Z","title":"Convergence rate analysis for averaged fixed point iterations in the presence of H\\\"older regularity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.06823","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:a4f704c7a1a2444423e3fe7643ed1a163fb6d190a617d40175a450bf7fcf8a7c","target":"record","created_at":"2026-05-18T00:08:05Z","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":"e0bdbc43458c0e10ec4e5a83d6efb530ded7021947844c1af55267f00aa64453","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-10-23T04:38:27Z","title_canon_sha256":"0f7371f517629c773037978b7382b791d323114101fc202c18e51804e5bd1c44"},"schema_version":"1.0","source":{"id":"1510.06823","kind":"arxiv","version":3}},"canonical_sha256":"f542370c45a1ca50354db035a4cd5580f77004a69ea3184536761a2e2a0f20b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f542370c45a1ca50354db035a4cd5580f77004a69ea3184536761a2e2a0f20b7","first_computed_at":"2026-05-18T00:08:05.463232Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:05.463232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EdrvwKq+NgzvKCSd1teK4E4FjT7ABmZE/YnyCsvqWRlqaqi+Pe71ivarB+ZI1goA79fICU9R56CvzK0nswyQDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:05.463761Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.06823","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4f704c7a1a2444423e3fe7643ed1a163fb6d190a617d40175a450bf7fcf8a7c","sha256:04659be3aff52c6550f48a0f1e225a61fa20ba4f1e4561592f23aaf36e0c5da1"],"state_sha256":"c4cbf9004bd3f38bfa159ad9c0cd747de8f5a3a6fb16b132ef6797784c844cd7"}